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DTSTART;TZID=America/New_York:20251015T170000
DTEND;TZID=America/New_York:20251015T180000
DTSTAMP:20260417T151445
CREATED:20250311T134919Z
LAST-MODIFIED:20251021T134849Z
UID:10003657-1760547600-1760551200@cmsa.fas.harvard.edu
SUMMARY:Millennium Prize Problems Lecture - Sourav Chatterjee: Yang-Mills and the foundations of quantum field theory
DESCRIPTION:Millennium Prize Problems Lecture  \nDate: October 15\, 2025 \nTime: 5:00–6:00 pm \nLocation: Harvard Science Center Hall D\, 1 Oxford St.\, Cambridge MA \nSpeaker: Sourav Chatterjee\, Stanford University \nTitle: Yang-Mills and the foundations of quantum field theory \nAbstract: Yang-Mills theories are the building blocks of the Standard Model of quantum mechanics\, which is the best available model for our universe at the quantum scale. Yet\, these theories do not have a rigorous mathematical foundation. Physical calculations are based on perturbation theory\, but there are various phenomena that are believed to be out of the reach of perturbative arguments. Building a mathematical foundation is\, therefore\, important even from the physics point of view. A program with this objective\, known as “constructive field theory”\, was initiated in the 1960s. In spite of many successes\, the program has not reached its original goal. Completing this program is the Clay Millennium Prize problem of Yang-Mills existence and mass gap. I will give a general introduction to the main questions\, and an overview of exciting recent progress that has rejuvenated the quest for a solution in the last ten years. \nRead more about the Yang-Mills Existence and Mass Gap at the Clay Math website. \nOrganizers: Martin Bridson\, Clay Mathematics Institute | Dan Freed\, Harvard University and CMSA | Mike Hopkins\, Harvard University \n\n                   \n\nMillennium Prize Problems Lecture Series
URL:https://cmsa.fas.harvard.edu/event/clay_101425/
LOCATION:Harvard Science Center Hall D\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Millennium Prize Problems Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Chatterjee_web_ad.2-scaled.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251016T140000
DTEND;TZID=America/New_York:20251016T150000
DTSTAMP:20260417T151445
CREATED:20250911T184527Z
LAST-MODIFIED:20251006T162709Z
UID:10003790-1760623200-1760626800@cmsa.fas.harvard.edu
SUMMARY:Lech's inequality and stability of local rings
DESCRIPTION:Algebra Seminar \nSpeaker: Linquan Ma (Purdue University) \nTitle: Lech’s inequality and stability of local rings \nAbstract: We explore Lech’s inequality relating the colength and multiplicity of m-primary ideals in a Noetherian local ring (R\,m). We introduce a natural invariant that measures the sharpness of Lech’s inequality and show its connections with singularities of asymptotically semistable varieties and singularities arising from the MMP. We compute this invariant in various examples. This is joint work with Ilya Smirnov. \n 
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_101625/
LOCATION:Virtual
CATEGORIES:Algebra Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebra-Seminar-10.16.25.docx-1-1-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251016T160000
DTEND;TZID=America/New_York:20251016T170000
DTSTAMP:20260417T151446
CREATED:20250904T162550Z
LAST-MODIFIED:20251014T150012Z
UID:10003780-1760630400-1760634000@cmsa.fas.harvard.edu
SUMMARY:Differential Geometry and Physics Seminar
DESCRIPTION:Differential Geometry and Physics Seminar  \nSpeaker: Andy Neitzke\, Yale \nTitle: Abelianization of tau functions \nAbstract: The symplectic and hyperkahler geometry of moduli spaces of flat connections over Riemann surfaces is in a sense quantized by the theory of isomonodromic tau functions. These functions in turn arise as partition functions in the conformal field theory of twisted free fermions. I will describe a new scheme for computing these tau functions via abelianization\, and what it produces in one simple example\, related to the Painleve I equation. This scheme is joint work with Qianyu Hao. The talk is intended to be self-contained (you don’t have to know in advance what a tau function or a conformal field theory is). \n  \n 
URL:https://cmsa.fas.harvard.edu/event/dgphys_101625/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Differential Geometry and Physics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/DG-Physics-Seminar-10.16.2025-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251017T120000
DTEND;TZID=America/New_York:20251017T130000
DTSTAMP:20260417T151446
CREATED:20250827T141359Z
LAST-MODIFIED:20251010T180544Z
UID:10003766-1760702400-1760706000@cmsa.fas.harvard.edu
SUMMARY:DMFT\, Two Point Correlations of Resolvents\, and Applications to Machine Learning Theory
DESCRIPTION:Member Seminar \nSpeaker: Blake Bordelon \nTitle: DMFT\, Two Point Correlations of Resolvents\, and Applications to Machine Learning Theory \nAbstract: Machine learning algorithms evolve the parameters of a model in a high dimensional and disordered loss landscape. To characterize the effects of random initialization of model parameters\, randomly sampled training data\, and the effect of SGD noise\, it often is useful to invoke ideas from random matrix theory and the physics of disordered systems. In this seminar\, I describe a general idea\, known as dynamical mean field theory (DMFT) which describes the evolution of a disordered dynamical system in infinite dimensions. I will briefly describe simple examples of interest to theoretical neuroscientists and machine learning theorists. For linear dynamical systems\, I will show that this method characterizes the typical case trajectory in terms of two point correlations of resolvent matrices evaluated at different frequencies. This bispectral object can account for puzzling effects such as late time divergence of gradient descent at the interpolation threshold (when parameters = dataset size) despite the Jacobian of the dynamics having real and non-positive eigenvalues. I will then describe a novel two point correlation result for general free products of the form M = O B O^T A for O sampled from the Haar measure. I will use this result to characterize the exact asymptotics of the performance of a linear transformer trained to perform in-context linear regression on “generic” (randomly rotated) covariance matrices.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101725/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.17.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251017T130000
DTEND;TZID=America/New_York:20251017T160000
DTSTAMP:20260417T151446
CREATED:20250930T134721Z
LAST-MODIFIED:20251014T133421Z
UID:10003800-1760706000-1760716800@cmsa.fas.harvard.edu
SUMMARY:Freedman Seminar: Michael Freedman\, CMSA & Bowen Yang\, CMSA
DESCRIPTION:Freedman Seminar \nSpeaker: Michael Freedman\, Harvard CMSA \nTitle: Sullivan’s work on Lipschitz structures \nAbstract: I’ll begin with an elementary\, but now little known\, piece of PL topology: engulfing. John Stalling used it to give an alternative proof of the high dimensional Poincare conjecture. Then I’ll explain Dennis Sullivan’s enhancement of Kirby’s torus trick (which relies on engulfing.) I’ll note an open question regarding Lipschitz structures on 4-manifolds. \n  \nSpeaker: Bowen Yang\, CMSA \nTitle: Quantum Cellular Automata and Algebraic L-Theory \nAbstract: Quantum cellular automata (QCAs) are models of reversible quantum dynamics that preserve locality; they can be thought of as quantum analogues of classical cellular automata\, but with much richer structure. I will describe a classification of the Clifford subclass of QCAs using methods from algebraic L-theory. The main result identifies the group of Clifford QCAs\, up to natural equivalences\, with L-theory homology of the underlying space. This gives a conceptual explanation of previously observed periodic patterns in lattice models and extends the picture to more general spaces. I will outline the ideas behind the construction and indicate how the framework connects topology\, operator algebras\, and quantum information. If time permits\, I will also comment on what is known — and unknown — about the general (non-Clifford) case.
URL:https://cmsa.fas.harvard.edu/event/freedman_101725/
LOCATION:Virtual
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-10.17.25.docx-1-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251020T150000
DTEND;TZID=America/New_York:20251020T160000
DTSTAMP:20260417T151446
CREATED:20250924T183004Z
LAST-MODIFIED:20251016T160042Z
UID:10003797-1760972400-1760976000@cmsa.fas.harvard.edu
SUMMARY:Categorical 't Hooft expansion and Chiral Algebras
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Adrian López-Raven\, Perimeter \nTitle: Categorical ‘t Hooft expansion and Chiral Algebras \nAbstract: In https://arxiv.org/abs/2411.00760\, we show how holographic dual B-model backgrounds can be systematically derived from the ‘t Hooft expansion of specific families of chiral algebras. The resulting holographic dual backgrounds are typically non-commutative and appear to be novel. In this talk I’ll review certain aspects of our construction. In particular\, we’ll review how to build a category of D-branes for the String Theory dual\, starting from the planar limit of the chiral algebra. Given its generality\, I’ll emphasize the potential utility of the construction in the study of weak coupling holography for general theories with a large N limit. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/qft_102025/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-10.20.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251020T163000
DTEND;TZID=America/New_York:20251020T173000
DTSTAMP:20260417T151446
CREATED:20250912T180641Z
LAST-MODIFIED:20251030T151928Z
UID:10003752-1760977800-1760981400@cmsa.fas.harvard.edu
SUMMARY:Math Science Lectures in Honor of Raoul Bott | Dennis Gaitsgory\, MPIM | Function-theoretic implications of geometric Langlands
DESCRIPTION:Two talks on Function-theoretic implications of geometric Langlands\nDates: October 20 & 21\, 2025 \nTime: 4:30–5:30 pm \nLocation: Science Center Lecture Hall A and via Webinar \n  \nSpeaker: Dennis Gaitsgory\, Max Planck Institute for Mathematics \nAbstract: The recently established geometric Langlands equivalence implies an explicit description of the space of (unramified) automorphic functions in terms of Langlands parameters. In these lectures\, we will derive these description and explain how far we can go with it in order to deduce some expected properties of automorphic functions\, e.g.\, Ramanujan and Arthur multiplicity conjectures. This is joint work with Vincent Lafforgue and Sam Raskin. \n  \nLecture 1: Monday\, October 20\, 2025\nFrom geometric to classical Langlands \n \n  \nLecture 2: Tuesday\, October 21\, 2025\nAnalytic properties of automorphic functions as seen from algebraic geometry \n \n  \n\nHarvard Mathematics Professor Raoul Bott (1923 – 2005)\, was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem\, the Morse–Bott functions which he used in this context\, and the Borel–Bott–Weil theorem.
URL:https://cmsa.fas.harvard.edu/event/mathscibott_2025/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Event,Math Science Lectures in Honor of Raoul Bott,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Bott-Lecture_2025.v2-scaled.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251021T163000
DTEND;TZID=America/New_York:20251021T173000
DTSTAMP:20260417T151446
CREATED:20250912T180816Z
LAST-MODIFIED:20251030T152043Z
UID:10003753-1761064200-1761067800@cmsa.fas.harvard.edu
SUMMARY:Math Science Lectures in Honor of Raoul Bott | Dennis Gaitsgory\, MPIM | Function-theoretic implications of geometric Langlands
DESCRIPTION:Two talks on Function-theoretic implications of geometric Langlands\nDates: October 20 & 21\, 2025 \nTime: 4:30–5:30 pm \nLocation: Science Center Lecture Hall A and via Webinar \nSpeaker: Dennis Gaitsgory\, Max Planck Institute for Mathematics \nAbstract: The recently established geometric Langlands equivalence implies an explicit description of the space of (unramified) automorphic functions in terms of Langlands parameters. In these lectures\, we will derive these description and explain how far we can go with it in order to deduce some expected properties of automorphic functions\, e.g.\, Ramanujan and Arthur multiplicity conjectures. This is joint work with Vincent Lafforgue and Sam Raskin. \n  \nLecture 1: Monday\, October 20\, 2025\nFunction-theoretic implications of geometric Langlands: From geometric to classical Langlands \n \n  \nLecture 2: Tuesday\, October 21\, 2025\nFunction-theoretic implications of geometric Langlands: Analytic properties of automorphic functions as seen from algebraic geometry \n \n\nHarvard Mathematics Professor Raoul Bott (1923 – 2005)\, was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem\, the Morse–Bott functions which he used in this context\, and the Borel–Bott–Weil theorem.
URL:https://cmsa.fas.harvard.edu/event/mathscibott_2025-2/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Event,Math Science Lectures in Honor of Raoul Bott,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Bott-Lecture_2025-scaled.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251022T120000
DTEND;TZID=America/New_York:20251022T130000
DTSTAMP:20260417T151446
CREATED:20251002T141005Z
LAST-MODIFIED:20251003T205211Z
UID:10003804-1761134400-1761138000@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Thomas Grimm
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Thomas Grimm\, Utrecht & CMSA \nTopic: What is o-minimality and what is it good for?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_102225/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Q-A-Seminar-10.22.2025-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251022T140000
DTEND;TZID=America/New_York:20251022T150000
DTSTAMP:20260417T151446
CREATED:20251008T132005Z
LAST-MODIFIED:20251008T133142Z
UID:10003808-1761141600-1761145200@cmsa.fas.harvard.edu
SUMMARY:The Carleson project: A collaborative formalization
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: María Inés de Frutos Fernández\, Mathematical Institute\, University of Bonn \nTitle: The Carleson project: A collaborative formalization \nAbstract: A well-known result in Fourier analysis establishes that the partial Fourier sums of a smooth periodic function $f$ converge uniformly to $f$\, but the situation is a lot more subtle for e.g. continuous functions. However\, in 1966 Carleson proved that they do converge at almost all points for $L^2$ periodic functions on the real line. Carleson’s proof is famously hard to read\, and there are no known easy proofs of this theorem. As a large collaborative project\, we have formalized in Lean a generalization of Carleson’s theorem in the setting of doubling metric measure spaces (proven in 2023)\, and Carleson’s original result as a corollary. In this talk I will give an overview of the project\, with a focus on how the collaboration was organized. \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_102225/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.22.2025-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251023T140000
DTEND;TZID=America/New_York:20251023T150000
DTSTAMP:20260417T151446
CREATED:20250911T184605Z
LAST-MODIFIED:20251021T143543Z
UID:10003791-1761228000-1761231600@cmsa.fas.harvard.edu
SUMMARY:Character sheaves on the loop Lie algebra and its global implications
DESCRIPTION:Algebra Seminar \nSpeaker: Zhiwei Yun\, MIT \nTitle: Character sheaves on the loop Lie algebra and its global implications \nAbstract: Motivated by Lusztig’s definition of character sheaves on a reductive Lie algebra\, we propose a definition of character sheaves on the loop Lie algebra. The construction can be viewed as a p-adic analogue of the orbit method\, and the resulting sheaves are closely related to characters of supercuspidal representations of J.K.Yu. Further\, the construction suggests a definition of wildly ramified Hitchin moduli spaces suitable for the study of ramified geometric Langlands. This is joint work with Bao Chau Ngo. \n 
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_102325/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebra Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebra-Seminar-10.23.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251023T160000
DTEND;TZID=America/New_York:20251023T170000
DTSTAMP:20260417T151446
CREATED:20250904T162649Z
LAST-MODIFIED:20251021T144005Z
UID:10003781-1761235200-1761238800@cmsa.fas.harvard.edu
SUMMARY:On some new irrationality results
DESCRIPTION:Differential Geometry and Physics Seminar  \nSpeaker: Ron Donagi\, UPenn \nTitle: On some new irrationality results \nAbstract: An algebraic variety X is rational if a Zariski-open subset of X is isomorphic to a Zariski-open subset of projective space. A weaker property is unirationality: X is unirational if a Zariski-open subset of projective space maps onto a Zariski-open subset of X. These properties are equivalent in dimensions 1 and 2. In the seventies it was discovered that they are not equivalent in dimension 3\, as several different approaches succeeded in proving irrationality of some unirational varieties. The theory of Hodge atoms\, recently developed by Katzarkov\, Kontsevich\, Pantev and Yu\, uses ideas from mirror symmetry and quantum cohomology to exhibit new birational invariants capable of proving irrationality of some 4-dimensional unirational varieties. We illustrate the power of this new technique by applying it to the 4 dimensional intersection of quadrics in P^7. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/dgphys_102325/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Differential Geometry and Physics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/DG-Physics-Seminar-10.23.2025.docx-1-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251024T120000
DTEND;TZID=America/New_York:20251024T130000
DTSTAMP:20260417T151446
CREATED:20250827T141425Z
LAST-MODIFIED:20251020T181711Z
UID:10003767-1761307200-1761310800@cmsa.fas.harvard.edu
SUMMARY:Analytic Spread of Binomial Edge Ideals
DESCRIPTION:Member Seminar \nSpeaker: Stephen Landsittel\, CMSA \nTitle: Analytic Spread of Binomial Edge Ideals \nAbstract: To an ideal J in a polynomial ring R over a field K we associate its analytic spread \ell(J)\, which is the dimension of the fiber cone F(J) of J. When J is graded and generated in a single degree d\, then F(J) is a finite type K-algebra. \nTo a graph G we associate its binomial edge ideal: J_G:= (x_i y_j – x_jy_i | {i\,j} is an edge of G). \nIn this talk we will discuss recent work where sharp bounds are given for \ell(J_G) and we compute the exact value when G is a pseudoforest. We accomplish this by computing the transcendence degree trdeg_{K} F(J)\, of the fiber cone over K.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-102425/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.24.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251027T150000
DTEND;TZID=America/New_York:20251027T160000
DTSTAMP:20260417T151446
CREATED:20250924T183029Z
LAST-MODIFIED:20251024T144939Z
UID:10003798-1761577200-1761580800@cmsa.fas.harvard.edu
SUMMARY:de Rham Theory in Derived Differential Geometry
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Grigorii Taroian\, U Toronto \nTitle: de Rham Theory in Derived Differential Geometry \nAbstract: In the talk\, I will describe recent progress in building a version of de Rham theory for derived manifolds and derived differentiable stacks.\nDerived differential geometry is a nascent field applying techniques from derived algebraic geometry to the study of spaces with smooth structures. As such\, it serves as a natural home for studying objects arising in BV formalism. For instance\, concepts such as critical loci of action functionals or their quotients by gauge actions can be naturally interpreted as derived differentiable stacks.\nIn our work\, we build a version of de Rham theory for these spaces and prove a version of the de Rham isomorphism. Due to the highly singular nature of all objects involved\, developing such a theory is significantly more challenging than in the usual differential geometry\, and thus\, we construct our formalism with inspiration from algebraic geometry rather than classical differential topology. As a main application of the developed theory\, we obtain a version of the comparison morphism between de Rham and constant sheaf cohomology arising from the corresponding map of stacks. This should enable further developments\, with a view towards a fully-fledged theory of shifted symplectic structures for derived differentiable stacks.\nThe talk is based on a preprint of the same name\, arXiv:2505.03978.
URL:https://cmsa.fas.harvard.edu/event/qft_102725/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-10.27.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251027T163000
DTEND;TZID=America/New_York:20251027T173000
DTSTAMP:20260417T151446
CREATED:20250911T192619Z
LAST-MODIFIED:20250911T193132Z
UID:10003793-1761582600-1761586200@cmsa.fas.harvard.edu
SUMMARY:Rigidity\, expansion and polytopes
DESCRIPTION:Colloquium \nSpeaker: Eran Nevo (Hebrew University of Jerusalem) \nTitle: Rigidity\, expansion and polytopes \nAbstract: Given a graph G and an embedding of its vertices in R^d\, what continuous motions of the vertices preserve all edge lengths? Clearly all motions induced by an isometry of R^d do\, these are the trivial motions; are there any others? If the answer is NO for all (equivalently\, for one) generic embedding\, G is called d-rigid. \nWhat are the d-rigid graphs? \nThis problem has been extensively studied since the 70s\, and is still widely open for d≥3. It is studied mainly from algebraic geometry and combinatorial points of view. Variants of it\, especially in dimensions 2 and 3\, are of importance also beyond mathematics\, e.g. in structural engineering\, computational biology and more. \nI will focus on a quantitative version of rigidity via spectral analysis of the related stiffness matrix\, including the construction of “rigidity expanders”\, generalizing expander graphs. Higher dimensional notions of rigidity and of stiffness matrices\, and their relation to the study of polytopes\, will be addressed too.
URL:https://cmsa.fas.harvard.edu/event/colloquium_102725/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.27.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251028T161500
DTEND;TZID=America/New_York:20251028T183000
DTSTAMP:20260417T151446
CREATED:20251021T201853Z
LAST-MODIFIED:20251027T135640Z
UID:10003818-1761668100-1761676200@cmsa.fas.harvard.edu
SUMMARY:Geometry and Quantum Theory Seminar
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeakers: (1) Elliott Gesteau\, CMSA (60 min) and  (2) Sanjay Raman\, Harvard (30 min) \n(1) Title: Holography for closed universes \nAbstract: Recent advances in holography and black hole physics have prompted a number of new puzzles related to the physics of closed universes\, which can be argued to have a one-dimensional Hilbert space of states from various perspectives. In this talk I will review this new set of puzzles\, with an emphasis of the mathematical questions that they seem to raise. \n  \n(2) Title: Non-supersymmetric branes\, bordism\, and fractional charges \nAbstract: We dive a little deeper into the non-supersymmetric brane configurations studied in Kaidi-Tachikawa-Yonekura (2024). We study the gravitational analogues of the branes in the aforementioned paper\, relating them to relative defects predicted by the Cobordism Conjecture\, and we argue for the existence of objects carrying fractional heterotic string and M2-brane charge.
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_102825/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, 02138
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-10.28.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251030T140000
DTEND;TZID=America/New_York:20251030T150000
DTSTAMP:20260417T151446
CREATED:20251014T143046Z
LAST-MODIFIED:20251030T144718Z
UID:10003812-1761832800-1761836400@cmsa.fas.harvard.edu
SUMMARY:Affine Springer fibers and representations
DESCRIPTION:Algebra Seminar \nSpeaker: Roman Bezrukavnikov\, MIT \nTitle: Affine Springer fibers and representations \nAbstract: Relating representation categories of interest\, such of modules over the quantum group\, to topology of loop spaces has been an important theme in representation theory for some decades. I will describe a result of this sort involving a geometric object that has not appeared in this context until now\, an affine Springer fiber\, and mention its applications. Based on a joint work with Pablo Boixeda Alvarez\, Michael McBreen and Zhiwei Yun. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_103025/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebra Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebra-Seminar-10.30.25.docx-2-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251030T160000
DTEND;TZID=America/New_York:20251030T170000
DTSTAMP:20260417T151446
CREATED:20250904T162918Z
LAST-MODIFIED:20251027T145519Z
UID:10003782-1761840000-1761843600@cmsa.fas.harvard.edu
SUMMARY:RCD structures on singular Kahler varieties
DESCRIPTION:Differential Geometry and Physics Seminar  \nSpeaker: Jian Song\, Rutgers University \nTitle: RCD structures on singular Kahler varieties \nAbstract: Let X be a 3-dimensional projective variety with klt singularities. We prove that every singular Kahler metric on X with bounded Nash entropy and Ricci curvature bounded below induces a unique compact RCD space homeomorphic to the projective variety X itself. In particular\, singular Kahler- Einstein spaces of complex dimension 3 with bounded Nash entropy are compact RCD spaces topologically and holomorphically equivalent to the underlying projective variety.  Such results establish connections among algebraic\, geometric and analytic structures of klt singularities from birational geometry and provide abundant examples of RCD spaces from algebraic geometry via complex Monge-Ampere equations.
URL:https://cmsa.fas.harvard.edu/event/dgphys_103025/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Differential Geometry and Physics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/DG-Physics-Seminar-10.30.2025-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251031T120000
DTEND;TZID=America/New_York:20251031T130000
DTSTAMP:20260417T151446
CREATED:20250827T141457Z
LAST-MODIFIED:20251027T151940Z
UID:10003768-1761912000-1761915600@cmsa.fas.harvard.edu
SUMMARY:Skein remain the same
DESCRIPTION:Member Seminar \nSpeaker: Sunghyuk Park\, CMSA \nTitle: Skein remain the same \nAbstract: The count of holomorphic curves in a Calabi-Yau 3-fold ending on a Lagrangian is famously not deformation invariant\, but Ekholm and Shende have shown that it can be made invariant by counting in the skein. Given a 3-manifold M and a branched cover arising from the projection of a Lagrangian 3-manifold L in the cotangent bundle of M\, we use the skein-valued curve count to construct a map from the skein of M to that of L. When M and L are products of surfaces and intervals\, deforming L within the space of Lagrangians yields a skein-valued lift of the Kontsevich-Soibelman wall-crossing formula. After all\, the skeins remain the same. Based on joint work (arXiv:2510.19041) with Tobias Ekholm\, Pietro Longhi\, and Vivek Shende. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-103125/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.31.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251104T161500
DTEND;TZID=America/New_York:20251104T183000
DTSTAMP:20260417T151446
CREATED:20251021T201937Z
LAST-MODIFIED:20251031T151517Z
UID:10003819-1762272900-1762281000@cmsa.fas.harvard.edu
SUMMARY:A fully local extension of Chern-Simons theory
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Dan Freed \nTitle: A fully local extension of Chern-Simons theory \nAbstract: The Reshetikhin-Turaev-Witten invariants of 3-manifolds fit into a 3-dimensional topological field theory that also attaches invariants to 2-manifolds and 1-manifolds. It has long been asked to extend to invariants of 0-manifolds as well\, a question that often takes the form: What does Chern-Simons theory attach to a point?. In joint work with Claudia Scheimbauer and Constantin Teleman we use the cobordism hypothesis to construct a fully local version of Chern-Simons theory. We also consider different versions with different tangential structures\, as I will explain.
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_11425/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, 02138
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-11.4.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251105T120000
DTEND;TZID=America/New_York:20251105T130000
DTSTAMP:20260417T151446
CREATED:20251014T151053Z
LAST-MODIFIED:20251014T151917Z
UID:10003817-1762344000-1762347600@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Paul Seidel\, MIT
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Paul Seidel\, MIT \nTopic: Fukaya categories of Landau-Ginzburg models
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_11525/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Q-A-Seminar-11.5.2025-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251105T140000
DTEND;TZID=America/New_York:20251105T150000
DTSTAMP:20260417T151446
CREATED:20251027T142022Z
LAST-MODIFIED:20251027T144043Z
UID:10003826-1762351200-1762354800@cmsa.fas.harvard.edu
SUMMARY:Discovery of unstable singularity with machine precision
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Yongji Wang\, NYU Courant Institute of Mathematical Sciences \nTitle: Discovery of unstable singularity with machine precision \nAbstract: Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations\, such as the 3D Euler equations\, develop infinite gradients from smooth initial conditions. Historically\, numerical approaches have primarily identified stable singularities. However\, these are not expected to exist for key open problems\, such as the boundary-free Euler and Navier-Stokes cases\, namely the Millennium Prize problem. For these problems\, the true challenge lies in finding unstable singularities\, which are exceptionally elusive\, as any tiny perturbation can divert the system from its blow-up trajectory. \nIn this talk\, I will present a new computational framework which has led to the first systematic discovery of new families of unstable singularities in various fluid equations. Our approach merges curated machine learning architectures with a multi-stage training scheme and a high-precision Gauss-Newton optimizer\, creating a powerful tool for navigating the complex landscape of nonlinear PDEs. Beyond discovering these singularities\, the precision of this method is another key breakthrough\, achieving unprecedented accuracies on the order of $O(10^{-13})$—a level constrained only by the round-off errors of the GPU hardware. This level of precision meets the stringent requirements for rigorous mathematical validation of the discovered solution via computer-assisted proofs\, offering a new pathway to resolving long-standing challenges in mathematical physics. \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_11525/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-11.5.2025-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251106T160000
DTEND;TZID=America/New_York:20251106T170000
DTSTAMP:20260417T151446
CREATED:20250904T163021Z
LAST-MODIFIED:20251104T160806Z
UID:10003784-1762444800-1762448400@cmsa.fas.harvard.edu
SUMMARY:Dimension Reduction and Adiabatic Limits of Generalized ASD Instantons
DESCRIPTION:Differential Geometry and Physics Seminar  \nSpeaker: Dylan Galt\, Harvard \nTitle: Dimension Reduction and Adiabatic Limits of Generalized ASD Instantons \nAbstract: I will begin by explaining a dimension reduction result for Tian’s generalized ASD instantons over product manifolds\, which generalizes work of Yuanqi Wang on codimension-one reduction and includes the cases of G2 and Spin(7) instantons as well as degree zero Hermitian-Yang-Mills connections. The proof is inspired by a simple observation about the Yang-Mills energy and suggests a natural adiabatic picture for these generalized ASD connections. I will describe ongoing work towards establishing such an adiabatic scheme\, emphasizing some of the complications that arise in the general case and explaining what can be said for G2 instantons. Everything I will talk about is joint work with my collaborator Langte Ma. \n 
URL:https://cmsa.fas.harvard.edu/event/dgphys_11625/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Differential Geometry and Physics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/DG-Physics-Seminar-11.6.2025.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251107T120000
DTEND;TZID=America/New_York:20251107T130000
DTSTAMP:20260417T151446
CREATED:20250827T141526Z
LAST-MODIFIED:20251103T161856Z
UID:10003769-1762516800-1762520400@cmsa.fas.harvard.edu
SUMMARY:Classification of 2D Stabilizer States
DESCRIPTION:Member Seminar \nSpeaker: Bowen Yang \nTitle: Classification of 2D Stabilizer States \nAbstract: I will explain how translation-invariant two-dimensional stabilizer states are completely classified by finite abelian groups with nondegenerate quadratic forms—that is\, by abelian anyon theories. The proof uses the algebraic structure of stabilizer codes as modules over Laurent polynomial rings\, revealing how their physical features reflect in this module-theoretic framework. arXiv:2509.10418
URL:https://cmsa.fas.harvard.edu/event/member-seminar-11725/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-11.7.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251110T150000
DTEND;TZID=America/New_York:20251110T160000
DTSTAMP:20260417T151446
CREATED:20251014T143715Z
LAST-MODIFIED:20251103T155540Z
UID:10003814-1762786800-1762790400@cmsa.fas.harvard.edu
SUMMARY:The Moyal bracket and the BV cohomology of the spinning particle
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Ezra Getzler\, Northwestern \nTitle: The Moyal bracket and the BV cohomology of the spinning particle \nAbstract: The spinning particle is the one-dimensional reduction of the Neveu-Schwartz-Ramond superstring. It consists of a supersymmetric particle moving in a one-dimensional supergravity background\, and its quantization is the Hilbert superspace of harmonic spinors. (These models are classified by N\, the number of copies of fermionic fields. In this talk\, N=1. The extension to N=2 is work in progress with Ivo.) It is actually an AKSZ model (so a generalization of one-dimensional Chern-Simons)\, and so associated to a differential graded symplectic supermanifold\, by which we mean a pair (ω\,Q)\, where ω is a(n exact) symplectic form and Q is an odd function of degree 1. The cohomology of the ring of functions of this supermanifold with differential the Poisson bracket  with Q determines the classical BV cohomology of the spinning particle\, so is important for understanding perturbative BV quantization of this model. I calculated this cohomology in earlier work for N=1\, and showed that it is somewhat bizarre\, with two series of cohomology classes in arbitrary negative degrees\, each a copy of the functions on the target manifold. \nIn the study of quantum BFV\, we should instead consider the Moyal bracket on the target\, and lift Q to an element Q satisfying [Q\,Q]=0. The cohomology of the differential [Q\,-] is the Moyal cohomology of the differential graded symplectic supermanifold. (This lift corresponds to the choice of a Spinc structure on the target manifold.) In this talk\, I prove that the Moyal cohomology\, unlike the Poisson cohomology\, is well-behaved: in the spectral sequence from Poisson to Moyal cohomology\, the extra cohomology classes of negative degree cancel each other pairwise at the E1 page. \n 
URL:https://cmsa.fas.harvard.edu/event/qft_111025/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-11.10.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251111T161500
DTEND;TZID=America/New_York:20251111T183000
DTSTAMP:20260417T151446
CREATED:20251021T202013Z
LAST-MODIFIED:20251110T161345Z
UID:10003820-1762877700-1762885800@cmsa.fas.harvard.edu
SUMMARY:Khovanov homology from KLRW algebras
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Sunghyuk Park\, CMSA \nTitle: Khovanov homology from KLRW algebras \nAbstract: This is the first in a four-part series\, organized together with Vasily Krylov\, Sebastian Haney\, and Lorenzo Riva\, aimed at understanding Aganagic’s categorification of quantum link invariants through Coulomb branches and homological mirror symmetry. In this first talk\, I will lay the algebraic background for this story by explaining how Khovanov homology can be understood in terms of higher representation theory via Khovanov-Lauda-Rouquier-Webster (KLRW) algebras.
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_111125/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, 02138
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-11.11.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251112T090000
DTEND;TZID=America/New_York:20251114T170000
DTSTAMP:20260417T151446
CREATED:20250502T181545Z
LAST-MODIFIED:20251113T214753Z
UID:10003745-1762938000-1763139600@cmsa.fas.harvard.edu
SUMMARY:Geometry Meets Physics: Finiteness\, Tameness\, and Complexity
DESCRIPTION:Geometry Meets Physics: Finiteness\, Tameness\, and Complexity \nDates: November 12–14\, 2025 \nLocation: CMSA G10\, 20 Garden Street\, Cambridge MA 02138 \n(note: this event is in-person only) \nFiniteness is a fundamental property in consistent physical theories. From the earliest days of quantum field theory and string theory\, the drive to eliminate unphysical infinities has been a guiding principle. More recently\, finiteness has emerged as a key criterion for constraining effective theories that can be embedded in quantum gravity.  Formulating and testing these constraints remains a central challenge in current research. \nIn parallel\, mathematics has made remarkable advanced in addressing finiteness questions using tame geometry. Built on the framework of o-minimal structures\, tame geometry offers a precise language for describing objects of finite geometric complexity. Recent developments\, such as sharp o-minimality\, go further by introducing a quantitative notion of complexity\, opening new directions for analyzing finiteness in mathematics and physics alike. \nThis workshop brings together mathematicians and physicists to exchange ideas\, explore new perspectives\, and spark collaborations at the interface of geometry\, logic\, and fundamental physics. \nInvited Speakers \n\nVijay Balasubramanian (UPenn)\nGregorio Baldi (CNRS\, IMJ-PRG & IAS)\nGal Binyamini (Weizmann Institute & IAS)\nRaf Cluckers (Lille\, France)\nMatilda Delgado (Max Planck Institute Munich)\nBruno Klingler (Humboldt University\, Berlin & IAS)\nAdele Padgett (Vienna)\nDavid Prieto (Utrecht)\nWashington Taylor (MIT)\nDavid Urbanik (IHES\, France & IAS)\nCumrun Vafa (Harvard)\nMick van Vliet (Utrecht)\nBenny Zak (Weizmann Institute & IAS)\n\nOrganizers: Thomas Grimm\, Harvard CMSA & Utrecht University | Gal Binyamini\, Weizmann Institute & IAS | Bruno Klingler\, Humboldt University\, Berlin & IAS \n  \nSchedule \n(download pdf) \nWednesday Nov. 12\, 2025 \n8:30–8:55 am\nMorning refreshments (Common Room) \n8:55–9:00 am\nIntroductions \n9:00–10:30 am\nLecture\nSpeaker: Gal Binyamini\, Weizmann Institute & IAS\nTitle: O-minimality: finiteness and complexity\nAbstract: O-minimality is a mathematical formalism of “tame geometry”: a geometry where every set has finite geometric complexity. I will give an introduction to o-minimality in general\, and to quantitative variants where one measures the complexity of sets in terms of some natural parameters. I’ll try to focus on the main examples that potentially come up in the interaction with physics\, and describe the state of the art and some conjectures. \n10:30–11:00 am\nBreak \n11:00 am–12:00 pm\nSpeaker: Benny Zak\, Weizmann Institute & IAS\nTitle: Analytic tameness – complex cells\nAbstract: Complex cells are a complex anayltic version of cells from o-minimality\, invented by Binyamini and Novikov. We aim to introduce complex cells\, and demonstrate their usefullness in quantifying the analytic information present in a complex set. If time permits\, we will discuss applications of this theory. \n12:00–1:00 pm\nCatered Lunch (Common Room) \n1:00–2:30 pm\nLecture\nSpeakers: David Prieto and Mick van Vliet\, Utrecht\nTitle: Tameness and Complexity in Physical Theories\nAbstract: We give an introductory overview of recent applications of o-minimality to physics\, focusing on quantum field theories and quantum gravity. In the first part of the lecture we explain how o-minimality makes a first appearance in physical theories when considering amplitudes in quantum field theory. In the second part\, we concentrate on a class of theories where finiteness principles seem to be essential\, namely the quantum field theories which are consistent with quantum gravity. We review some of these finiteness principles and interpret them through the lens of the o-minimal framework. Along the way\, we highlight recent progress in this direction\, as well as open questions to explore in the future. \n2:30–3:00 pm\nBreak with refreshments (Common Room) \n3:00–4:00 pm\nSpeaker: Matilda Delgado\, Max Planck Institute Munich\nTitle: Dualities and the Compactifiability of Moduli Space\nAbstract:  After introducing (self-)dualities in string theory and their action on the field content & spectrum of the theory\, I will present the notion of compactifiability for the moduli space of massless fields as the condition that its volume is finite or grows no faster than Euclidean space. I will argue that compactifiability generically implies the existence of non-trivial dualities by providing evidence from string theory. Moreover\, I will explain how one can connect compactifiability to the condition that the spectrum of objects charged under the duality group transform in a semisimple representation. Finally\, I will provide a bottom-up argument for compactifiability\, and argue that it (at least in supersymmetric cases) can be explained by the finiteness of the number of massless states upon compactification to 1D. Based on arXiv:2412.03640. \n5:00 PM\nMillennium Lecture and Reception: Pierre Deligne (IAS) (Science Center Hall D)\nTitle: What is the Hodge conjecture? \n  \nThursday\, Nov. 13\, 2025 \n8:30–9:00 am\nMorning refreshments (Common Room) \n9:00–10:30 am\nLecture\nSpeaker: Bruno Klingler\, Humboldt University\, Berlin & IAS\nTitle: Tame geometry and Hodge theory\nAbstract: I will give an introduction to applications of o-minimality in complex geometry\, in particular in Hodge theory. \n10:30–11:00 am\nBreak \n11:00 am–12:00 pm\nSpeaker: Cumrun Vafa\, Harvard\nTitle: The Swampland Program \n12:00–1:30 pm\nCatered Lunch (Common Room) \n1:30–2:30 pm\nSpeaker: Gregorio Baldi\, CNRS\, IMJ-PRG & IAS\nTitle: The Hodge locus\nAbstract: We will survey various recent results around the distribution of the Hodge locus of a (mixed) variation of Hodge structures. Various concrete applications to moduli spaces will also be presented. \n2:30–3:00 pm\nBreak with refreshments (Common Room) \n3:00–4:00 pm\nSpeaker: Vijay Balasubramanian\, U Penn\nTitle: Chaos and complexity in quantum dynamics \n4:30–5:30\nDiscussion/Q&A session \n6:30 PM\nDinner: Changsho Restaurant\, 1712 Massachusetts Ave.\, Cambridge\, MA 02138 \n  \nFriday Nov. 14\, 2025 \n8:30–9:00 am\nMorning refreshments (Common Room) \n9:00–10:00 am\nSpeaker: Washington Taylor\, MIT\nTitle: Finiteness\, connectivity\, and the power of fibrations in the Calabi-Yau landscape \n10:00–10:30am\nBreak \n10:30–11:30 am\nSpeaker: Adele Padgett\, Vienna\nTitle: Tameness of multisummable series\nAbstract: There are sophisticated theories of summability that map divergent series solutions of differential or functional equations to solutions that are holomorphic in sector-like domains. Van den Dries and Speissegger proved that functions obtained from real multisummable power series have tame geometric behavior when restricted to the real numbers. It would be desirable to know that these functions are also tame on their whole sector-like domains\, but recently Speissegger and I proved that these functions are in general only tame on part of their domains. I will present this result and discuss the domains on which some examples are tame\, including the Stirling series which appears in the asymptotic expansion of the Gamma function. In this talk\, “tame” means definable in an o-minimal structure. \n11:30 am–1:00 pm\nCatered Lunch (Common Room) \n1:00–2:00 pm\nSpeaker: Raf Cluckers\, Lille\, France\nTitle:  Finiteness and tameness in (non-archimedean) geometry\nAbstract: Non-archimedean geometry work with orders of magnitude rather than with precise measurements. The former works for example with orders of vanishing of functions\, and the latter typically works with real or complex numbers. I will discuss recent progress on non-archimedean tame geometry. I will present analogues of o-minimality\, of Pila-Wilkie’s o-minimal counting results\, and of other finiteness results\, in non-archimedean settings. \n2:00–2:30 pm\nBreak with refreshments (Common Room) \n2:30–3:30 pm\nSpeaker: David Urbanik\, IHES\, France & IAS\nTitle: Degrees of Hodge Loci \n\n    \n  \n 
URL:https://cmsa.fas.harvard.edu/event/geophys/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event,Workshop
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Geophys_poster.4-scaled.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251112T170000
DTEND;TZID=America/New_York:20251112T180000
DTSTAMP:20260417T151446
CREATED:20250311T134920Z
LAST-MODIFIED:20251201T154039Z
UID:10003658-1762966800-1762970400@cmsa.fas.harvard.edu
SUMMARY:Millennium Prize Problems Lecture - Pierre Deligne: What is the Hodge conjecture?
DESCRIPTION:  \n \nDate: November 12\, 2025 \nTime: 5:00–6:00 pm \nLocation: Harvard Science Center Hall D\, 1 Oxford St.\, Cambridge MA \nSpeaker: Pierre Deligne\, Institute for Advanced Study \nTitle: What is the Hodge conjecture? \nAbstract: The Hodge conjecture is about projective non-singular complex algebraic varieties. It characterizes the cohomology classes coming from algebraic cycles. I will explain these terms\, tell why the conjecture is so hard to attack\, and why we care. \n  \nSeries Pamphlet (pdf) \nRead more about the Hodge Conjecture at the Clay Math website. \nOrganizers: Martin Bridson\, Clay Mathematics Institute | Dan Freed\, Harvard University and CMSA | Mike Hopkins\, Harvard University \n\n                   \n\nMillennium Prize Problems Lecture Series
URL:https://cmsa.fas.harvard.edu/event/clay_111225/
LOCATION:Harvard Science Center Hall D\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Millennium Prize Problems Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Deligne_web-ad-scaled.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251114T130000
DTEND;TZID=America/New_York:20251114T160000
DTSTAMP:20260417T151446
CREATED:20251104T215810Z
LAST-MODIFIED:20251105T144505Z
UID:10003832-1763125200-1763136000@cmsa.fas.harvard.edu
SUMMARY:Freedman Seminar: Michael Freedman\, CMSA & Bowen Yang\, CMSA
DESCRIPTION:Freedman Seminar \nSpeaker: Michael Freedman\, Harvard CMSA \nTitle: Sullivan’s work on Lipschitz structures Part II (but self-contained) \n  \nSpeaker: Bowen Yang\, CMSA \nTitle: Deligne and Sullivan’s work on complex bundles with discrete structure group \n 
URL:https://cmsa.fas.harvard.edu/event/freedman_111425/
LOCATION:Virtual
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-11.14.25.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251117T090000
DTEND;TZID=America/New_York:20251119T170000
DTSTAMP:20260417T151446
CREATED:20250502T182846Z
LAST-MODIFIED:20251215T145740Z
UID:10003749-1763370000-1763571600@cmsa.fas.harvard.edu
SUMMARY:Conference on Geometry and Statistics
DESCRIPTION:Conference on Geometry and Statistics \nDates: November 17–19\, 2025 \nLocation: CMSA G10\, 20 Garden Street\, Cambridge MA & via Zoom \n  \nSpeakers \n\nCharles Fefferman\, Princeton University\nStephan Huckemann\, Georg-August Universität Göttingen\nSungkyu Jung\, Seoul National University\nKei Kobayashi\, Keio University\nClément Levrard\, Université de Rennes\nKer-Chau Li\, University of California\, Los Angeles\nRong Ma\, Harvard University\nSteve Marron\, University of North Carolina\nEzra Miller\, Duke University\nHans-Georg Müller\, University of California\, Davis\nWilderich Tuschmann\, Karlsruhe Institute of Technology\nMelanie Weber\, Harvard University\nAndrew Wood\, Australian National University\nHorng-Tzer Yau\, Harvard University\n\nOrganizer: Zhigang Yao\, National University of Singapore \n  \nYoutube Playlist \n  \nSCHEDULE \ndownload pdf \nMonday\, Nov. 17\, 2025 \n9:00–9:25 am\nMorning refreshments \n9:25–9:30 am\nIntroductions \n9:30–10:30 am\nSpeaker: Stephan Huckemann\, Georg-August Universität Göttingen\nTitle: The Probability of the Cut Locus of a Fréchet Mean\nAbstract: We show that the cut locus of a Fréchet mean of a random variable on a connected and complete Riemanian manifold has zero probability\, a result known previously in special cases (Le and Barden\, 2014) and conjectured in general. The proof is based on first order and second order considerations\, where the latter are based on a recent result by Générau (2020) on “Laplacians in the barrier sense”. This generalizes to Fréchet p-means for p > 2. The former allow also to rule out stickiness on Riemannian manifolds\, and for generalization to 1 <= p < 2\, with a conjecture. We close with discussing and conjecturing extensions to noncomplete manifolds and more general metric spaces. This is joint work with Alexander Lytchak. \n\nGénérau\, F. (2020). Laplacian of the distance function on the cut locus on a Riemannian manifold. Nonlinearity 33(8)\, 3928.\nLe\, H. and D. Barden (2014).  On the measure of the cut locus of a Fréchet mean. Bulletin of the London Mathematical Society 46(4)\, 698–708.\nLytchak\, A. and S. F. Huckemann (2025). Zero mass at the cut locus of a Fréchet mean on a Riemannian manifold. arXiv preprint arXiv:2508.00747.\n\n10:30–10:45 am\nbreak \n10:45 am–11:45 am\nSpeaker: Hans-Georg Müller\, University of California\, Davis\nTitle: Conformal Inference for Random Objects\nAbstract: The underlying probability measure of random objects\, i.e.\, metric-space-valued random variables\, can be probed by distance profiles. These are one-dimensional distributions of probability mass falling into balls of increasing radius. In a regression setting with Euclidean covariates X and responses Y that are random objects\, one can consider conditional Fréchet means that can be implemented with Fréchet regression and also conditional distance profiles\, conditioning on X. Conditional distance profiles can then be leveraged to obtain conditional average transport costs\, the expected cost for transporting a fixed conditional distance profile to a randomly selected conditional distance profile. The conditional average transport costs can then be utilized to obtain conditional conformity scores. In conjunction with the split conformal algorithm these scores lead to conditional prediction sets located in the object space with asymptotic conditional validity and attractive finite sample behavior. Based on joint work Hang Zhou (UNC). \n11:45 am–1:15 pm\nLunch (Catered) \n1:15–2:15 pm\nSpeaker: Horng-Tzer Yau\, Harvard\nTitle: Ramanujan property of random regular graphs and delocalization of random band matrices\nAbstract: In this lecture\, we review recent works on random matrices. The first result is about the normalized adjacency matrix of a random $d$-regular graph on $N$ vertices with any fixed degree $d\geq 3$ and denote its eigenvalues as $\lambda_1=d/\sqrt{d-1}\geq \lambda_2\geq\lambda_3\cdots\geq \lambda_N$. We establish the edge universality for random $d$-regular graphs\, namely\, the distributions of $\lambda_2$ and $-\lambda_N$ converge to the Tracy-Widom$_1$ distribution associated with the Gaussian Orthogonal Ensemble. As a consequence\, for sufficiently large $N$\, approximately $69\%$ of $d$-regular graphs on $N$ vertices.\nare Ramanujan\, meaning $\max\{\lambda_2\,|\lambda_N|\}\leq 2$. This resolves a conjecture by Sarnak and Miller-Novikoff-Sabelli\nThe second result concerns $ N \times N$ Hermitian $d$-dimensional random band matrices with band width $W$. In the bulk of the spectrum and in the large $ N $ limit\, we prove that all $ L^2 $- normalized eigenvectors are delocalized in all dimensions under suitable conditions on $W$ and $N$. In addition\, we proved that the eigenvalue statistics are given by those of the Gaussian unitary ensemble. \n2:15–2:45 pm\nbreak with refreshments \n2:45–3:45 pm\nSpeaker: Clément Levrard\, Université de Rennes\nTitle: Optimal reach estimation\nAbstract: The reach of an embedded submanifold\, a notion that dates back to the famous work Curvature measures of H. Federer\, may be understood as a scale under which the submanifold is flat enough so that traditional Euclidean techniques in statistics locally apply\, up to some approximation. I will expose several ways to estimate the reach from sample (on the submanifold)\, some of them being optimal from the point of view of minimax estimation theory. Along the way\, intermediate estimation problems of local and global quantities will arise (curvature estimation\, weak feature size estimation\, distance estimation\, etc.)\, for which various phenomenons can occur from a statistical point of view (different convergence rates\, inconsistency). This will be an opportunity to provide a selective overview of the state of the art on these issues. \n4:30–5:30 pm\nCMSA Colloquium\nSpeaker: Zhigang Yao (National University of Singapore)\nTitle: Interaction of Statistics and Geometry: A New Landscape for Data Science\nAbstract:  Classical statistics views data as real numbers or vectors in Euclidean space\, but modern challenges increasingly involve data with intrinsic geometric structures. A central problem in this direction is manifold fitting\, with origins in H. Whitney’s work of the 1930s. The Geometric Whitney Problems ask: given a set\, when can we construct a smooth 𝑑-dimensional manifold that approximates it\, and how accurately can we estimate it?\nIn this talk\, I will discuss recent progress on manifold fitting and its role in bridging geometry and data science. While many existing methods rely on restrictive assumptions\, the manifold hypothesis—that data often lie near non-Euclidean structures—remains fundamental in modern statistical learning. I will highlight both theoretical insights and algorithmic challenges\, drawing on recent works with\, as well as ongoing research. \nYoutube video \n  \nTuesday\, Nov. 18\, 2025 \n9:00–9:30 am\nMorning refreshments \n9:30–10:30 am\nSpeaker: Charles Fefferman\, Princeton University (via Zoom)\nTitle: Extrinsic and intrinsic manifold learning\, old and new\nAbstract: The talk will include an exposition of the old paper “Testing the manifold hypothesis”\, joint work with S. Mitter and H. Narayanan\, on extrinsic manifold learning (the manifold to be learned is assumed to be embedded in a high-dimensional Euclidean space). The talk will also include a new result on intrinsic manifold learning (the manifold to be learned is not assumed to be embedded\, and the data consist of intrinsic distances corrupted by noise)\, provided the result is proven by the time of the conference. \n10:30–10:45 am\nbreak \n10:45 am–11:45 am\nSpeaker: Steve Marron\, University of North Carolina\nTitle: Data Integration Via Analysis of Manifolds (DIVAM)\nAbstract: A major challenge in the age of Big Data is the integration of disparate data types into a single data analysis. That was tackled by Data Integration Via Analysis of Subspaces (DIVAS) in the context of data blocks measured on a common set of experimental cases. Joint variation was defined in terms of modes of variation having identical scores across data blocks. DIVAS allowed mathematically rigorous formulation of individual variation within each data block in terms of individual modes. The goal of DIVAM is to intrinsically extend the DIVAS approach to data objects lying in manifolds\, such as shape data. \n11:45 am–1:15 pm\nLunch Break \n1:15–2:15 pm\nSpeaker: Ker-Chau Li\, University of California\, Los Angeles\nTitle: Investigation of Data clouds: From Galton’s Ellipses to Explainable AI (XAI)\, modeling or molding?\nAbstract: Francis Galton’s seminal 1886 visualization of regression toward the mean in trait inheritance is arguably the first and most influential example of geometric thinking applied to statistical modeling. The pioneering geometric insight driving Galton’s use of elliptical contours to discover the bivariate normal distribution laid down the foundation for classic multivariate analysis (e.g.\, PCA\, canonical correlation) and profoundly impacts modern methods like diffusion models.\nStatistical models\, particularly those based on parsimony\, are effective for characterizing data distribution and facilitating scientific rule induction. However\, the rise of unstructured big data (like images) has challenged these parsimonious approaches\, necessitating the use of deep learning models. These models\, containing billions of parameters\, sacrifice transparency to excel in prediction. Seeking solutions to this “black-box” dilemma is now the heart of Explainable AI (XAI).\nLeveraging the simplicity of elementary geometric concepts\, this talk will present a new path toward interpretable and parsimonious XAI. Unstructured big data is highly plastic. Our approach moves beyond the standard data modeling perspective—which answers what the data is—and introduces a novel data molding perspective. This shift is key to unlocking the full potential of data’s plasticity\, allowing us to effectively answer the crucial question: what the data can be used for.\nI will first discuss a connection between manifold learning and my earlier works\, helical confounding and liquid association. I will then turn to the data molding perspective and present two novel notions: mold-compliance and artificial-trait configurative-generation (ATCG). These notions guide our recent efforts in formulating novel algorithms for image data investigation\, addressing issues like prediction validity and within-class heterogeneity. Data molding entails a dramatically different feature space extraction\, which consequently shifts the subsequent investigation on the data clouds from out-of-distribution (OOD) to mold-violation\, and from UMAP clustering to ATCG-induced hierarchical clustering. \n2:15–2:45 pm\nbreak with refreshments \n2:45–3:45 pm\nSpeaker: Andrew Wood\, Australian National University\nTitle: Empirical likelihood methods for Fréchet means on open books\nAbstract: The open book is a simple example of a stratified space that captures some (but not all) of the properties of stratified spaces. Central limit theory for open books plus relevant background is given by Hotz et al. (2013\, Annals of Applied Probability). In this talk I will describe some basic inference procedures for Fréchet means in open books based on empirical likelihood (Owen\, book\, 2001). Empirical likelihood (EL) is a type of nonparametric likelihood that can be useful for many types of data\, including manifold-valued data and data from stratified spaces. An EL approach to basic inference for Fréchet means will be described. In particular\, it will be shown how the non-regularity in the geometry of open books can result in non-regular behaviour in Wilks’s theorem (i.e. the large sample likelihood ratio test). The talk will also discuss difficulties in extending the EL inference theory from open books to more general stratified spaces\, where the difference in dimension of adjacent strata can be 2 or more. For discussion of more general stratified spaces than open books\, see the orthant spaces discussed in Barden and Le (2018\, Proc of London Math Society) and the general stratified space setting considered by Mattingly et al. (2023\, arxiv). \n3:45–4:00 pm\nbreak \n4:00–5:00 pm\nSpeaker: Wilderich Tuschmann\, Karlsruhe Institute of Technology\nTitle: A Spectator’s Perspective on the Manifold Hypothesis\nAbstract: At its core\, the Manifold Hypothesis asserts that real-world\, high-dimensional data is not uniformly or randomly distributed throughout its high-dimensional “ambient” space\, but concentrated on or near a low-dimensional manifold (or a collection of manifolds) embedded within that high-dimensional ambient space.\nIn my talk\, I will discuss reasons and facts that speak for as well as against this hypothesis and also address geometric alternatives. \n  \nWednesday\, Nov. 19\, 2025 \n9:00–9:30 am\nMorning refreshments \n9:30–10:30 am\nSpeaker: Melanie Weber\, Harvard University\nTitle: Ricci Curvature\, Ricci Flow\, and the Geometry of Learning\nAbstract: Geometric structure in data plays a crucial role in machine learning. In this talk\, we study this observation through the lens of Ricci curvature and its associated Ricci flow. We start by reviewing a discrete notion of Ricci curvature introduced by Ollivier and the geometric flow that it induces. We further discuss the relationship between discrete Ricci curvature and its continuous counterpart via discrete-to-continuum consistency results\, which imply that discrete Ricci curvature can provably characterize the geometry of a data manifold based on a finite sample. This provides a theoretical foundation for several applications of discrete Ricci curvature in machine learning\, two of which we discuss in the remainder of this talk. First\, we analyze learned feature representations in deep neural networks and show that they transform during training in ways that closely resemble a discrete Ricci flow. Our analysis reveals that nonlinear activations shape class separability and suggests geometry-informed training principles such as early stopping and depth selection. Second\, we turn to deep learning on graphs\, where we address representational limitations of state of the art graph neural networks through curvature-based data augmentations. We show that augmenting input graphs with geometric information provably increases the representational power of such models and yields performance gains in practice. \n10:30–10:45 am\nbreak \n10:45 am–11:45 am\nSpeaker: Ezra Miller\, Duke University\nTitle: Extracting bar lengths from multiparameter persistent homology\nAbstract: Persistent homology in one parameter can be summarized using bar codes or persistence diagrams\, which are elementary gadgets with many features amenable to vectorization and hence statistical analysis. For example\, early work with Bendich\, Marron\, Pieloch\, and Skwerer showed how to extract meaningful statistics from the top 100 bar lengths in persistent homology summaries of brain arteries. The story for persistent homology with multiple parameters\, on the other hand\, is still developing. Although it has the potential to be much more flexible and informative\, multipersistence has structural issues that present fundamental mathematical challenges. There is no consensus on what might be meant by a “bar”\, let alone “the top 100 bar lengths”. This talk recalls the basics of single and multiparameter persistent homology and discusses some of the mathematical issues\, including obstacles and potential routes forward. \n11:45 am–1:15 pm\nLunch Break \n1:15–2:15 pm\nSpeaker: Kei Kobayashi\, Keio University\nTitle: Metric Transformations of Data Spaces: Curvature Control and Related Developments\nAbstract: We present our proposed method of increasing the accuracy of data analysis by means of two transformations of the metric of the data space. The first transformation is based on the curve length defined by the integral of the power of the density function\, which can be computed approximately using an empirical graph; the second transformation can be interpreted as the extrinsic distance when the data space is embedded in a metric cone. The advantage of both distance transformations is that the hyperparameters allow the curvature to be monotonically transformed in a specific sense. Some statistical applications of these transformations and theoretical justifications are presented. Detailed analyses of the geodesics obtained by this method for several simple probability distributions will also be presented. The main part of this work is based on joint works with Henry P. Wynn. \n2:15–2:45 pm\nbreak with refreshments \n2:45–3:45 pm\nSpeaker: Sungkyu Jung\, Seoul National University\nTitle: Generalized Frechet means with random minimizing domains and its strong consistency\nAbstract: In this talk\, I will discuss a novel extension of Frechet means\, referred to as generalized  Frechet  means\, as a comprehensive framework for describing the characteristics of random elements. The generalized Frechet mean is defined as the minimizer of a cost function\, and the framework encompasses various extensions of Frechet means that have appeared in the literature. The most distinctive feature of the proposed framework is that it allows the domain of minimization for the empirical generalized Frechet means to be random and different from that of its population counterpart. This flexibility broadens the applicability of the Frechet mean framework to various statistical scenarios\, including sequential dimension reduction for non-Euclidean data. We establish a strong consistency theorem for generalized Frechet means. Applications such as verifying the consistency of principal geodesic analysis on the hypersphere\, compositional principal component analysis on the composition space\, and k-medoids clustering for data on a metric space will be discussed. \n3:45–4:00 pm\nbreak \n4:00–5:00 pm\nSpeaker: Rong Ma\, Harvard University\nTitle: Modern Nonlinear Embedding Methods Unpacked\nAbstract: Learning and representing low-dimensional structures from noisy\, high-dimensional data is a cornerstone of modern data science. Stochastic neighbor embedding algorithms\, a family of nonlinear dimensionality reduction and data visualization methods\, with t-SNE and UMAP as two leading examples\, have become very popular in recent years. Yet despite their wide applications\, these methods remain subject to points of debate\, including limited theoretical understanding\, ambiguous interpretations\, and sensitivity to tuning parameters. In this talk\, I will present our recent efforts to decipher and improve these nonlinear embedding approaches. Our key results include a rigorous theoretical framework that uncovers the intrinsic mechanisms\, large-sample limits\, and fundamental principles underlying these algorithms; a set of theory-informed practical guidelines for their principled use in trustworthy biological discovery; and a collection of new algorithms that address current limitations and improve performance in areas such as bias reduction and stability. Throughout the talk\, I will highlight how these advances not only deepen our theoretical understanding but also open new avenues for scientific discovery.
URL:https://cmsa.fas.harvard.edu/event/geostat_2025/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Conference
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