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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211020T093000
DTEND;TZID=America/New_York:20211020T103000
DTSTAMP:20260506T232335
CREATED:20240214T043359Z
LAST-MODIFIED:20240507T193206Z
UID:10002530-1634722200-1634725800@cmsa.fas.harvard.edu
SUMMARY:Categorification and applications
DESCRIPTION:Speaker: Peng Shan (Tsinghua University)\n\n\n\nTitle: Categorification and applications \nAbstract: I will give a survey of the program of categorification for quantum groups\, some of its recent development and applications to representation theory.
URL:https://cmsa.fas.harvard.edu/event/categorification-and-applications/
LOCATION:Virtual
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.20.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211021T153000
DTEND;TZID=America/New_York:20211021T170000
DTSTAMP:20260506T232335
CREATED:20240214T102900Z
LAST-MODIFIED:20240301T091902Z
UID:10002672-1634830200-1634835600@cmsa.fas.harvard.edu
SUMMARY:Electric-magnetic duality and the Geometric Langlands duality
DESCRIPTION:Title: Electric-magnetic duality and the Geometric Langlands duality \nAbstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.
URL:https://cmsa.fas.harvard.edu/event/10-21-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211021T184400
DTEND;TZID=America/New_York:20211021T204400
DTSTAMP:20260506T232335
CREATED:20240214T082555Z
LAST-MODIFIED:20240301T104328Z
UID:10002587-1634841840-1634849040@cmsa.fas.harvard.edu
SUMMARY:10/21/2021 Interdisciplinary Science Seminar
DESCRIPTION:Title: Mathematical resolution of the Liouville conformal field theory. \nAbstract: The Liouville conformal field theory is a well-known beautiful quantum field theory in physics describing random surfaces. Only recently a mathematical approach based on a well-defined path integral to this theory has been proposed using probability by David\, Kupiainen\, Rhodes\, Vargas. \nMany works since the ’80s in theoretical physics (starting with Belavin-Polyakov-Zamolodchikov) tell us that conformal field theories in dimension 2 are in general « Integrable »\, the correlations functions are solutions of PDEs and can in principle be computed explicitely by using algebraic tools (vertex operator algebras\, representations of Virasoro algebras\, the theory of conformal blocks). However\, for Liouville Theory this was not done at the mathematical level by algebraic methods. \nI’ll explain how to combine probabilistic\, analytic and geometric tools to give explicit (although complicated) expressions for all the correlation functions on all Riemann surfaces in terms of certain holomorphic functions of the moduli parameters called conformal blocks\, and of the structure constant (3-point function on the sphere). This gives a concrete mathematical proof of the so-called conformal bootstrap and of Segal’s gluing axioms for this CFT. The idea is to break the path integral on a closed surface into path integrals on pairs of pants and reduce all correlation functions to the 3-point correlation function on the Riemann sphere $S^2$. This amounts in particular to prove a spectral resolution of a certain operator acting on $L^2(H^{-s}(S^1))$ where $H^{-s}(S^1)$ is the Sobolev space of order -s<0 equipped with a Gaussian measure\, which is viewed as the space of fields\, and to construct a certain representation of the Virasoro algebra into unbounded operators acting on this Hilbert space. \nThis is joint work with A. Kupiainen\, R. Rhodes and V. Vargas.
URL:https://cmsa.fas.harvard.edu/event/10-21-2021-interdisciplinary-science-seminar/
LOCATION:MA
CATEGORIES:Interdisciplinary Science Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211022T093000
DTEND;TZID=America/New_York:20211022T103000
DTSTAMP:20260506T232335
CREATED:20240213T105511Z
LAST-MODIFIED:20240304T101145Z
UID:10002466-1634895000-1634898600@cmsa.fas.harvard.edu
SUMMARY:The Large D Limit of Einstein’s Equations
DESCRIPTION:Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study\, with relatively simple techniques\, some of the thorniest problems in black hole physics\, such as the non-linear evolution of the instabilities of black strings and black branes\, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about\, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.
URL:https://cmsa.fas.harvard.edu/event/10-22-2021-general-relativity-seminar/
LOCATION:MA
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211022T093000
DTEND;TZID=America/New_York:20211022T103000
DTSTAMP:20260506T232335
CREATED:20240214T073722Z
LAST-MODIFIED:20240301T111559Z
UID:10002564-1634895000-1634898600@cmsa.fas.harvard.edu
SUMMARY:Wall-crossing from Higgs bundles to vortices
DESCRIPTION:Speaker: Du Pei \nTitle: Wall-crossing from Higgs bundles to vortices \nAbstract: Quantum field theories can often be used to uncover hidden algebraic structures in geometry and hidden geometric structures in algebra. In this talk\, I will demonstrate how such “wall-crossing” can relate the moduli space of Higgs bundles with the moduli space of vortices.
URL:https://cmsa.fas.harvard.edu/event/10-22-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211025T130000
DTEND;TZID=America/New_York:20211025T140000
DTSTAMP:20260506T232335
CREATED:20240214T093259Z
LAST-MODIFIED:20240301T082800Z
UID:10002633-1635166800-1635170400@cmsa.fas.harvard.edu
SUMMARY:Exploring the Holographic Swampland
DESCRIPTION:Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space\, such as LVS in type IIB or the DGKT flux vacua in type IIA\, the dual moduli conformal dimensions reduce to fixed values – in a certain sense\, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer\, for reasons we do not understand.
URL:https://cmsa.fas.harvard.edu/event/10-25-2021-swampland-seminar/
LOCATION:MA
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211026T090000
DTEND;TZID=America/New_York:20211026T100000
DTSTAMP:20260506T232335
CREATED:20240213T113529Z
LAST-MODIFIED:20240304T101126Z
UID:10002507-1635238800-1635242400@cmsa.fas.harvard.edu
SUMMARY:The n-queens problem
DESCRIPTION:Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another\, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture\, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and\, combined with our toroidal result\, completely settles a conjecture of Rivin\, Vardi and Zimmerman regarding both Q(n) and T(n). \nIn this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption. \nThis is joint work with Peter Keevash.
URL:https://cmsa.fas.harvard.edu/event/10-26-2021-combinatorics-physics-and-probability-seminar/
LOCATION:MA
CATEGORIES:Combinatorics Physics and Probability
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211026T130000
DTEND;TZID=America/New_York:20211026T140000
DTSTAMP:20260506T232335
CREATED:20240214T062643Z
LAST-MODIFIED:20240304T063155Z
UID:10002549-1635253200-1635256800@cmsa.fas.harvard.edu
SUMMARY:On singular Hilbert schemes of points
DESCRIPTION:Abstract: It is well known that the Hilbert schemes of points on smooth surfaces are smooth. In higher dimensions the Hilbert schemes of points are in general singular. In this talk we will present some examples and conjectures on the local structures of the Hilbert scheme of points on $\mathbb{P}^3$. As an application we study a conjecture of Wang-Zhou on the Euler characteristics of the tautological sheaves on Hilbert schemes of points.
URL:https://cmsa.fas.harvard.edu/event/on-singular-hilbert-schemes-of-points/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211027T093000
DTEND;TZID=America/New_York:20211027T103000
DTSTAMP:20260506T232335
CREATED:20240214T043101Z
LAST-MODIFIED:20240502T151724Z
UID:10002529-1635327000-1635330600@cmsa.fas.harvard.edu
SUMMARY:Anisotropy\, biased pairing theory and applications
DESCRIPTION:Speaker: Karim Adiprasito\, Hebrew University and University of Copenhagen \nTitle: Anisotropy\, biased pairing theory and applications \nAbstract: Not so long ago\, the relations between algebraic geometry and combinatorics were strictly governed by the former party\, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry\, specifically Hodge Theory. And so\, while we proved analogues for these results\, combinatorics felt subjugated to inspirations from outside of it.\nIn recent years\, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature\, we use intuitions from the Hall marriage theorem\, translated to algebra: once there\, they are statements about self-pairings\, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry\, which in turn established solutions to long-standing conjectures in combinatorics. \nI will survey this theory\, called biased pairing theory\, and new developments within it\, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki\, Vasiliki Petrotou and Johanna Steinmeyer.
URL:https://cmsa.fas.harvard.edu/event/anisotropy-biased-pairing-theory-and-applications/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.27.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211027T140000
DTEND;TZID=America/New_York:20211027T150000
DTSTAMP:20260506T232335
CREATED:20240214T093929Z
LAST-MODIFIED:20240517T193105Z
UID:10002641-1635343200-1635346800@cmsa.fas.harvard.edu
SUMMARY:Why explain mathematics to computers?
DESCRIPTION:Speaker: Patrick Massot\, Laboratoire de Mathématiques d’Orsay and CNRS \nTitle: Why explain mathematics to computers? \nAbstract: A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk I’ll describe what formalization looks like\, what kind of things it teaches us\, and how it could even turn out to be useful (in our usual sense of “useful”). This will not be a talk about foundations of mathematics\, and I won’t assume any prior knowledge about formalization.
URL:https://cmsa.fas.harvard.edu/event/10-27-2021-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.27.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211028T093000
DTEND;TZID=America/New_York:20211028T103000
DTSTAMP:20260506T232335
CREATED:20240213T112817Z
LAST-MODIFIED:20240304T102039Z
UID:10002500-1635413400-1635417000@cmsa.fas.harvard.edu
SUMMARY:The classical interior of charged black holes with AdS asymptotics
DESCRIPTION:Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations\, Cauchy horizons never form. We then consider charged scalars\, which are known to condense at low temperatures\, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity\, and there is no Cauchy horizon. Before reaching the singularity\, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion\, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations\, the number of Kasner inversions depends very sensitively on temperature\, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures\, the final Kasner exponent exhibits fractal-like behavior.
URL:https://cmsa.fas.harvard.edu/event/10-28-2021-general-relativity-seminar/
LOCATION:MA
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211028T130000
DTEND;TZID=America/New_York:20211028T143000
DTSTAMP:20260506T232335
CREATED:20240213T112644Z
LAST-MODIFIED:20240304T084647Z
UID:10002498-1635426000-1635431400@cmsa.fas.harvard.edu
SUMMARY:Drivers of Morphological Complexity
DESCRIPTION:Abstract: During development\, organisms interact with their natural habitats while undergoing morphological changes\, yet we know little about how the interplay between developing systems and their environments impacts animal morphogenesis. Cnidaria\, a basal animal lineage that includes sea anemones\, corals\, hydras\, and jellyfish\, offers unique insight into the development and evolution of morphological complexity.  In my talk\, I will introduce our research on “ethology of morphogenesis\,” a novel concept that links the behavior of organisms to the development of their size and shape at both cellular and biophysical levels\, opening new perspectives about the design principle of soft-bodied animals. In addition\, I will discuss a fascinating feature of cnidarian biology. For humans\, our genetic code determines that we will grow two arms and two legs. The same fate is true for all mammals. Similarly\, the number of fins of a fish or legs and wings of an insect is embedded in their genetic code. I will describe how sea anemones defy this rule. \nReferences\nAnniek Stokkermans\, Aditi Chakrabarti\, Ling Wang\, Prachiti Moghe\, Kaushikaram Subramanian\, Petrus Steenbergen\, Gregor Mönke\, Takashi Hiiragi\, Robert Prevedel\, L. Mahadevan\, and Aissam Ikmi. Ethology of morphogenesis reveals the design principles of cnidarian size and shape development. bioRxiv 2021.08.19.456976 \nIkmi A\, Steenbergen P\, Anzo M\, McMullen M\, Stokkermans M\, Ellington L\, and Gibson M (2020). Feeding-dependent tentacle development in the sea anemone Nematostella vectensis. Nature communications\, Sept 02; 11:4399 \nHe S\, Del Viso F\, Chen C\, Ikmi A\, Kroesen A\, Gibson MC (2018). An axial Hox code controls tissue segmentation and body patterning in Nematostella vectensis. Science\, Vol. 361\, Issue 6409\, pp. 1377-1380.\nIkmi A\, McKinney SA\, Delventhal KM\, Gibson MC (2014). TALEN and CRISPR/Cas9 mediated genome editing in the early-branching metazoan Nematostella vectensis. Nature communications. Nov 24; 5:5486.
URL:https://cmsa.fas.harvard.edu/event/drivers-of-morphological-complexity/
LOCATION:MA
CATEGORIES:Active Matter Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211028T184500
DTEND;TZID=America/New_York:20211028T204500
DTSTAMP:20260506T232335
CREATED:20240301T104157Z
LAST-MODIFIED:20240305T104709Z
UID:10002894-1635446700-1635453900@cmsa.fas.harvard.edu
SUMMARY:ARCH: Know What Your Machine Doesn’t Know
DESCRIPTION:Speaker: Jie Yang\, Delft University of Technology \nTitle: ARCH: Know What Your Machine Doesn’t Know \nAbstract: Despite their impressive performance\, machine learning systems remain prohibitively unreliable in safety-\, trust-\, and ethically sensitive domains. Recent discussions in different sub-fields of AI have reached the consensus of knowledge need in machine learning; few discussions have touched upon the diagnosis of what knowledge is needed. In this talk\, I will present our ongoing work on ARCH\, a knowledge-driven\, human-centered\, and reasoning-based tool\, for diagnosing the unknowns of a machine learning system. ARCH leverages human intelligence to create domain knowledge required for a given task and to describe the internal behavior of a machine learning system; it infers the missing or incorrect knowledge of the system with the built-in probabilistic\, abductive reasoning engine. ARCH is a generic tool that can be applied to machine learning in different contexts. In the talk\, I will present several applications in which ARCH is currently being developed and tested\, including health\, finance\, and smart buildings.
URL:https://cmsa.fas.harvard.edu/event/10-28-2021-interdisciplinary-science-seminar/
LOCATION:MA
CATEGORIES:Interdisciplinary Science Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211029T093000
DTEND;TZID=America/New_York:20211029T103000
DTSTAMP:20260506T232335
CREATED:20240214T073521Z
LAST-MODIFIED:20240301T111455Z
UID:10002563-1635499800-1635503400@cmsa.fas.harvard.edu
SUMMARY:The complex Monge-Ampere equation in K\”ahler geometry
DESCRIPTION:Speaker: Freid Tong \nTitle: The complex Monge-Ampere equation in Kahler geometry \nAbstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry\, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk\, I will introduce the complex Monge-Ampere equation and discuss the interplay between their analysis and geometry\, with a particular focus on the a priori C^0 estimates and their various applications. In the end\, I will also try to discuss some recent work with B. Guo and D.H. Phong on a new approach for proving sharp C^0 estimates for complex Monge-Ampere equations\, this new approach avoids the machinery of pluripotential theory that was previously necessary and has the advantage of generalizing to a large class of fully nonlinear equations.
URL:https://cmsa.fas.harvard.edu/event/10-29-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211029T120000
DTEND;TZID=America/New_York:20211029T130000
DTSTAMP:20260506T232335
CREATED:20240214T102641Z
LAST-MODIFIED:20240301T091452Z
UID:10002670-1635508800-1635512400@cmsa.fas.harvard.edu
SUMMARY:Anomaly resolution via decomposition
DESCRIPTION:Speaker: Eric Sharpe (Virginia Tech) \nTitle: Anomaly resolution via decomposition \nAbstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly\, for our purposes\, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition\, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups\, of which the extensions of [X/G] are examples.  After a review of decomposition\, we will see that decomposition implies that in (1+1) dimensions\, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.
URL:https://cmsa.fas.harvard.edu/event/10-29-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211029T120000
DTEND;TZID=America/New_York:20211029T130000
DTSTAMP:20260506T232335
CREATED:20240301T091725Z
LAST-MODIFIED:20240301T091725Z
UID:10002890-1635508800-1635512400@cmsa.fas.harvard.edu
SUMMARY:Integrability and chaos of 1+1d chiral edge states
DESCRIPTION:Speaker: Biao Lian (Princeton) \nTitle: Integrability and chaos of 1+1d chiral edge states \nAbstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states\, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states\, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions\, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models\, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly\, I will talk about the analytical and numerical study of the 4/3 FQH edge theory\, which shows unusual behavior in its integrability.
URL:https://cmsa.fas.harvard.edu/event/10-29-2021-quantum-matter-in-mathematics-and-physics-2/
LOCATION:MA
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211101T130000
DTEND;TZID=America/New_York:20211101T140000
DTSTAMP:20260506T232335
CREATED:20240214T092956Z
LAST-MODIFIED:20240301T081324Z
UID:10002631-1635771600-1635775200@cmsa.fas.harvard.edu
SUMMARY:Bubble instability of mIIA on AdS_4 x S^6
DESCRIPTION:Speaker: Pieter Bomans\, Princeton \nTitle: Bubble instability of mIIA on AdS_4 x S^6 \nAbstract: Recently\, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore\, they are stable against a variety of non-perturbative decay channels. Hence\, at this point\, they represent a serious challenge to the AdS swampland conjecture. In my talk\, I will review in detail the construction of these vacua as well as introduce a new decay channel\, ultimately sealing their fate as being unstable.
URL:https://cmsa.fas.harvard.edu/event/11-1-2021-swampland-seminar/
LOCATION:MA
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211102T093000
DTEND;TZID=America/New_York:20211102T103000
DTSTAMP:20260506T232335
CREATED:20240213T062436Z
LAST-MODIFIED:20240213T062436Z
UID:10002107-1635845400-1635849000@cmsa.fas.harvard.edu
SUMMARY:Counting invariant curves on a Calabi-Yau threefold with an involution
DESCRIPTION:Abstract: Gopakumar-Vafa invariants are integers n_beta(g) which give a virtual count of genus g curves in the class beta on a Calabi-Yau threefold. In this talk\, I will give a general overview of two of the sheaf-theoretic approaches to defining these invariants: via stable pairs a la Pandharipande-Thomas (PT) and via perverse sheaves a la Maulik-Toda (MT). I will then outline a parallel theory of Gopakumar-Vafa invariants for a Calabi-Yau threefold X with an involution. They are integers n_beta(g\,h) which give a virtual count of curves of genus g in the class beta which are invariant under the involution and whose quotient by the involution has genus h. I will give two definitions of n_beta(g\,h) which are conjectured to be equivalent\, one in terms of a version of PT theory\, and one in terms of a version of MT theory. These invariants can be computed and the conjecture proved in the case where X=SxC where S is an Abelian or K3 surface with a symplectic involution. In these cases\, the invariants are given by formulas expressed with Jacobi modular forms. In the case where S is an Abelian surface\, the specialization of n_beta(g\,h) to h=0 recovers the count of hyperelliptic curves on Abelian surfaces first computed by B-Oberdieck-Pandharipande-Yin. This is joint work with Stephen Pietromonaco.
URL:https://cmsa.fas.harvard.edu/event/counting-invariant-curves-on-a-calabi-yau-threefold-with-an-involution/
LOCATION:MA
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Jim-Bryan_poster_3Nov2021.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211102T130000
DTEND;TZID=America/New_York:20211102T140000
DTSTAMP:20260506T232335
CREATED:20240214T052811Z
LAST-MODIFIED:20240304T062921Z
UID:10002538-1635858000-1635861600@cmsa.fas.harvard.edu
SUMMARY:Gauss-Manin connection in disguise: Quasi Jacobi forms of index zero
DESCRIPTION:Abstract: We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomology with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations which are given as vector fields. In the case of elliptic curves we compute explicitly the Gauss-Manin connection and such vector fields. This is a joint work with J. Cao and R. Villaflor. (arXiv:2109.00587)
URL:https://cmsa.fas.harvard.edu/event/gauss-manin-connection-in-disguise-quasi-jacobi-forms-of-index-zero/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211103T093000
DTEND;TZID=America/New_York:20211103T103000
DTSTAMP:20260506T232335
CREATED:20240212T104227Z
LAST-MODIFIED:20240502T152621Z
UID:10002003-1635931800-1635935400@cmsa.fas.harvard.edu
SUMMARY:Hitchin map as spectrum of equivariant cohomology
DESCRIPTION:Speaker: Tamás Hausel (IST Austria) \nTitle: Hitchin map as spectrum of equivariant cohomology \nAbstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.
URL:https://cmsa.fas.harvard.edu/event/hitchin-map-as-spectrum-of-equivariant-cohomology/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-11.03.21-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211103T140000
DTEND;TZID=America/New_York:20211103T153000
DTSTAMP:20260506T232335
CREATED:20240214T102259Z
LAST-MODIFIED:20240301T091205Z
UID:10002667-1635948000-1635953400@cmsa.fas.harvard.edu
SUMMARY:Non-Invertible Duality Defects in 3+1 Dimensions
DESCRIPTION:Speaker: Clay Cordova (U Chicago) \nTitle: Non-Invertible Duality Defects in 3+1 Dimensions \nAbstract:  For any quantum system invariant under gauging a higher-form global symmetry\, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases\, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry\, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.
URL:https://cmsa.fas.harvard.edu/event/11-3-3021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211103T171200
DTEND;TZID=America/New_York:20211103T181200
DTSTAMP:20260506T232335
CREATED:20240214T094241Z
LAST-MODIFIED:20240813T155909Z
UID:10002643-1635959520-1635963120@cmsa.fas.harvard.edu
SUMMARY:When Computer Algebra Meets Satisfiability: A New Approach to Combinatorial Mathematics
DESCRIPTION:Speakers: Curtis Bright\, School of Computer Science\, University of Windsor and Vijay Ganesh\, Dept. of Electrical and Computer Engineering\, University of Waterloo \nTitle: When Computer Algebra Meets Satisfiability: A New Approach to Combinatorial Mathematics \nAbstract: Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their excellent search algorithms.  This talk will describe a new method for mathematical search that couples SAT solvers with computer algebra systems (CAS)\, thereby combining the expressiveness of CASs with the search power of SAT solvers.  This paradigm has led to a number of results on long-standing mathematical questions such as the first computer-verifiable resolution of Lam’s problem and the discovery of a new infinite class of Williamson matrices.
URL:https://cmsa.fas.harvard.edu/event/11-3-21-cmsa-new-technologies-in-mathematics/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-11.03.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211104T103000
DTEND;TZID=America/New_York:20211104T120000
DTSTAMP:20260506T232335
CREATED:20240214T101922Z
LAST-MODIFIED:20240301T091041Z
UID:10002665-1636021800-1636027200@cmsa.fas.harvard.edu
SUMMARY:Fusion Category Symmetries in Quantum Field Theory
DESCRIPTION:Speaker: Yifan Wang (NYU) \nTitle: Fusion Category Symmetries in Quantum Field Theory \nAbstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar inverti \n \nble symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting\, I’ll also comment on higher dimensional generalizations.
URL:https://cmsa.fas.harvard.edu/event/11-4-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:MA
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211104T130000
DTEND;TZID=America/New_York:20211104T140000
DTSTAMP:20260506T232335
CREATED:20240214T073728Z
LAST-MODIFIED:20240304T054749Z
UID:10002565-1636030800-1636034400@cmsa.fas.harvard.edu
SUMMARY:The stability of charged black holes
DESCRIPTION:Abstract: Black holes solutions in General Relativity are parametrized by their mass\, spin and charge. In this talk\, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally\, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole\, where the interaction between the radiations prevents the separability in modes.
URL:https://cmsa.fas.harvard.edu/event/11-4-2021-general-relativity-seminar/
LOCATION:MA
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211104T184600
DTEND;TZID=America/New_York:20211104T204600
DTSTAMP:20260506T232335
CREATED:20240214T080650Z
LAST-MODIFIED:20240301T103919Z
UID:10002580-1636051560-1636058760@cmsa.fas.harvard.edu
SUMMARY:11/4/21 CMSA Interdisciplinary Science Seminar
DESCRIPTION:Title: Exploring Invertibility in Image Processing and Restoration \nAbstract: Today’s smartphones have enabled numerous stunning visual effects from denoising to beautification\, and we can share high-quality JPEG images easily on the internet\, but it is still valuable for photographers and researchers to keep the original raw camera data for further post-processing (e.g.\, retouching) and analysis. However\, the huge size of raw data hinders its popularity in practice\, so can we almost perfectly restore the raw data from a compressed RGB image and thus avoid storing any raw data? This question leads us to design an invertible image signal processing pipeline. Then we further explore invertibility in other image processing and restoration tasks\, including image compression\, reversible image conversion (e.g.\, image-to-video conversion)\, and embedding novel views in a single JPEG image. We demonstrate that customized invertible neural networks are highly effective in these inherently non-invertible tasks.
URL:https://cmsa.fas.harvard.edu/event/11-4-21-cmsa-interdisciplinary-science-seminar/
LOCATION:MA
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-11.04.21-1583x2048-1-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211105T093000
DTEND;TZID=America/New_York:20211105T113000
DTSTAMP:20260506T232335
CREATED:20240214T073106Z
LAST-MODIFIED:20240301T111130Z
UID:10002562-1636104600-1636111800@cmsa.fas.harvard.edu
SUMMARY:The Greene-Plesser Construction Revisited
DESCRIPTION:Member Seminar  \nSpeaker: Chuck Doran \nTitle: The Greene-Plesser Construction Revisited \nAbstract: The first known construction of mirror pairs of Calabi-Yau manifolds was the Greene-Plesser “quotient and resolve” procedure which applies to pencils of hypersurfaces in projective space. We’ll review this approach\, uncover the hints it gives for some more general mirror constructions\, and describe a brand-new variant that applies to pencils of hypersurfaces in Grassmannians. This last is joint work with Tom Coates and Elana Kalashnikov (arXiv:2110.0727).
URL:https://cmsa.fas.harvard.edu/event/11-5-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211109T103000
DTEND;TZID=America/New_York:20211109T113000
DTSTAMP:20260506T232335
CREATED:20240213T062822Z
LAST-MODIFIED:20240304T062818Z
UID:10002112-1636453800-1636457400@cmsa.fas.harvard.edu
SUMMARY:Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds
DESCRIPTION:Abstract: Localization by cosection\, first introduced by Kiem-Li in 2010\, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.\nIn this talk\, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence\, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application\, the stable pair invariants of hyperkähler fourfolds\, constructed by Maulik-Cao-Toda\, vanish\, as expected.
URL:https://cmsa.fas.harvard.edu/event/cosection-localization-for-virtual-fundamental-classes-of-d-manifolds-and-donaldson-thomas-invariants-of-calabi-yau-fourfolds/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-Seminar-11.09.21-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211109T103000
DTEND;TZID=America/New_York:20211109T223000
DTSTAMP:20260506T232335
CREATED:20240304T062554Z
LAST-MODIFIED:20240304T062554Z
UID:10002897-1636453800-1636497000@cmsa.fas.harvard.edu
SUMMARY:Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds
DESCRIPTION:Speaker: Michail Savvas\, UT Austin \nTitle: Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds \nAbstract: Localization by cosection\, first introduced by Kiem-Li in 2010\, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.\nIn this talk\, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence\, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application\, the stable pair invariants of hyperkähler fourfolds\, constructed by Maulik-Cao-Toda\, vanish\, as expected. \n\n\n\nevent\n\n\nOrganizer: Seminars
URL:https://cmsa.fas.harvard.edu/event/11-9-21-cmsa-algebraic-geometry-in-string-theory-seminar/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211110T093000
DTEND;TZID=America/New_York:20211110T103000
DTSTAMP:20260506T232335
CREATED:20240212T104422Z
LAST-MODIFIED:20240502T153432Z
UID:10002006-1636536600-1636540200@cmsa.fas.harvard.edu
SUMMARY:Hypergraph decompositions and their applications
DESCRIPTION:Speaker: Peter Keevash\, Oxford \nTitle: Hypergraph decompositions and their applications \nAbstract: Many combinatorial objects can be thought of as a hypergraph decomposition\, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example\, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general\, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs\, which I proved in 2014\, states that\, bar finitely many exceptions\, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting\, which implies an approximate formula for the number of designs; in particular\, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects\, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem)\, whist tournaments or generalised Sudoku squares. In this talk\, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them. \n 
URL:https://cmsa.fas.harvard.edu/event/hypergraph-decompositions-and-their-applications/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-11.10.21-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211110T160000
DTEND;TZID=America/New_York:20211110T170000
DTSTAMP:20260506T232335
CREATED:20240213T063355Z
LAST-MODIFIED:20240213T063355Z
UID:10002116-1636560000-1636563600@cmsa.fas.harvard.edu
SUMMARY:Higher rank DT theory from rank 1
DESCRIPTION:Abstract: Fix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X. Along the way we also show they are determined by rank 0 invariants counting sheaves supported on surfaces in X. These invariants are predicted by S-duality to be governed by (vector-valued\, mock) modular forms.
URL:https://cmsa.fas.harvard.edu/event/higher-rank-dt-theory-from-rank-1/
LOCATION:MA
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/20211110_Richard-Thomas_poster-1.png
END:VEVENT
END:VCALENDAR