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DTSTART;TZID=America/New_York:20251201T163000
DTEND;TZID=America/New_York:20251201T173000
DTSTAMP:20260405T040127
CREATED:20251007T152747Z
LAST-MODIFIED:20251201T144411Z
UID:10003807-1764606600-1764610200@cmsa.fas.harvard.edu
SUMMARY:Asymptotic Theory of Attention: In-Context Learning and Sparse Token Detection
DESCRIPTION:Colloquium \nSpeaker: Yue M. Lu\, Harvard University \nTitle: Asymptotic Theory of Attention: In-Context Learning and Sparse Token Detection \nAbstract: Attention-based architectures exhibit striking emergent abilities—from learning tasks directly from context to detecting rare\, weak features in long sequences—yet a rigorous theory explaining these behaviors remains limited. In this talk\, I will present two recent exactly solvable models that develop a high-dimensional asymptotic theory of attention. \n(i) In-context learning. For linear attention pretrained on linear regression tasks\, we derive sharp asymptotics in a regime where token dimension\, context length\, and task diversity all scale proportionally\, while the number of pretraining examples scales quadratically. The resulting learning curve exhibits double descent and a phase transition separating a low-diversity memorization regime from a high-diversity regime of genuine in-context generalization. These predictions closely track empirical behavior in both linear-attention models and nonlinear Transformer architectures. \n(ii) Sparse-token classification. For detecting weak signals embedded in a small\, randomly located subset of tokens\, we analyze a single-layer attention classifier and determine its representational and learnability thresholds. Attention succeeds with only logarithmic signal scaling in the sequence length L\, outperforming linear baselines that require √L scaling. In a proportional high-dimensional regime\, we prove that two gradient descent steps yield nontrivial alignment between the query vector and the hidden signal\, leading to signal-adaptive attention. Exact formulas for the test error\, training loss\, and separability capacity quantify this advantage.
URL:https://cmsa.fas.harvard.edu/event/colloquium-12125/
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-12.1.2025-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251202T161500
DTEND;TZID=America/New_York:20251202T183000
DTSTAMP:20260405T040127
CREATED:20251021T202125Z
LAST-MODIFIED:20251201T192115Z
UID:10003822-1764692100-1764700200@cmsa.fas.harvard.edu
SUMMARY:Homological mirror symmetry for Coulomb branches
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Sebastian Haney\, Harvard \nTitle: Homological mirror symmetry for Coulomb branches \nAbstract: I will describe a result of Aganagic\, Danilenko\, Li\, Shende\, and Zhou which constructs a embeddings of certain cylindrical KLRW categories into Fukaya-Seidel categories of multiplicative Coulomb branches. This can be thought of as a homological mirror symmetry statement relating the Fukaya category of a multiplicative Coulomb branch to the derived category of a resolved additive Coulomb branch. I will describe the construction of the relevant Fukaya–Seidel categories\, and explain how the KRLW relations are realized by counts of holomorphic disks in symmetric products of surfaces. \n\n 
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_12225/
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-12.2.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251203T140000
DTEND;TZID=America/New_York:20251203T150000
DTSTAMP:20260405T040127
CREATED:20251110T191407Z
LAST-MODIFIED:20251110T225824Z
UID:10003833-1764770400-1764774000@cmsa.fas.harvard.edu
SUMMARY:Machine learning tools for mathematical discovery
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Adam Zsolt Wagner\, Google DeepMind \nTitle: Machine learning tools for mathematical discovery \nAbstract: I will discuss various ML tools we can use today to try to find interesting constructions to various mathematical problems. I will briefly mention simple reinforcement learning setups and PatternBoost\, but the talk will mainly focus on LLM-based tools such as FunSearch and AlphaEvolve. We will discuss the pros and cons of several of these methods\, and try to figure out which one is best for the problems we care about.\nJoint work with François Charton\, Jordan Ellenberg\, Bogdan Georgiev\, Javier Gómez-Serrano\, Terence Tao\, and Geordie Williamson.
URL:https://cmsa.fas.harvard.edu/event/newtech_12325/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-12.3.2025-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251203T170000
DTEND;TZID=America/New_York:20251203T180000
DTSTAMP:20260405T040128
CREATED:20250409T160258Z
LAST-MODIFIED:20251205T171720Z
UID:10003659-1764781200-1764784800@cmsa.fas.harvard.edu
SUMMARY:Millennium Prize Problems Lecture - Madhu Sudan: P vs NP Problem
DESCRIPTION:Pamphlet (pdf) \nSlides (pdf) \nDate: December 3\, 2025 \nTime: 5:00–6:00 pm \nLocation: Harvard Science Center Hall D\, 1 Oxford St.\, Cambridge MA \nSpeaker: Madhu Sudan\, Harvard University \nTitle: The P vs. NP problem: An Existential Question for Mathematics \nAt the beginning of the twentieth century\, in response to questions raised by Hilbert\, illustrious mathematicians such as Godel\, Church and Turing formalized the notion of theorems and proofs. Proofs were automatically verifiable while theorems are logical propositions for which proofs exist. The formal definition of a computer\, a definition that had strong influence on the later development of the technology\, was a by-product of the effort to define the phrase “automatically verifiable”! \nWhile the resulting theory had major implications already\, one notion was however missing in the early definitions. Proofs were meant to be easily verifiable\, while determining the truth of a proposition/conjecture (arguably a core task of mathematics) was not necessarily so. But what is “easiness” and how is it to be defined? While this was already hinted at by Godel in the 50s\, the notion was finally formalized in seminal works of Cook\, Levin and Karp in the early 70s. Central notions here included the adoption of the notion that polynomial time algorithms are (the only) tractable ones\, and the realization that algorithms seeking to remove the existential quantifier in the definition of a “theorem” lead naively to exponential time algorithms. But are there no sophisticated algorithms to search for proofs? This is the profound “Is P = NP?” question. \nIn this talk we will introduce the question and explain implications of resolutions of this question to the modern computing infrastructure\, to mathematics and other sciences. We will briefly describe the state of progress on this question and recent progress on weaker forms of this question. Finally we will also aim to connect this question\, and why one may believe that P != NP (proof search can not be automated) even in the face of accumulating evidence on the ability of computers to solve more and more complex mathematical problems\, which seem to implement brute force search in less than polynomial time. \n  \nRead more about the P vs NP Problem at the Clay Math website. \n  \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_12325/
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/Sudan_web-ad_CROP-scaled.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251204T120000
DTEND;TZID=America/New_York:20251204T130000
DTSTAMP:20260405T040128
CREATED:20250904T163130Z
LAST-MODIFIED:20251203T150446Z
UID:10003786-1764849600-1764853200@cmsa.fas.harvard.edu
SUMMARY:Towards a Dolbeault AGT correspondence
DESCRIPTION:Differential Geometry and Physics Seminar  \nSpeaker: Surya Raghavendran\, Yale \nTitle: Towards a Dolbeault AGT correspondence \nAbstract: The AGT correspondence and its extensions propose geometric constructions of vertex algebras and their modules from the cohomology of various moduli spaces of sheaves on surfaces. Physically\, the correspondence is illuminated throgh the holomorphic–topological twist of the six-dimensional N=(2\,0) superconformal field theories. In this talk\, I will describe a variant of AGT arising instead from the so-called minimal twist of these theories. In this setting\, the natural algebraic structures are holomorphic factorization algebras in three complex dimensions. From these\, one can extract an associative algebra together with a natural module\, which we conjecture to coincide with a quantization of the moduli of Higgs sheaves on surfaces. In examples\, this pair is furthermore expected to admit a Hodge–de Rham deformation to the Heisenberg algebra and its action on the cohomology of Hilbert schemes of surfaces\, as constructed by Grojnowski and Nakajima. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/dgphys_12425/
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-12.4.2025.docx-1-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251205T120000
DTEND;TZID=America/New_York:20251205T130000
DTSTAMP:20260405T040128
CREATED:20250827T142953Z
LAST-MODIFIED:20251202T160532Z
UID:10003772-1764936000-1764939600@cmsa.fas.harvard.edu
SUMMARY:A combinatorial formula for interpolation Macdonald polynomials
DESCRIPTION:Member Seminar \nSpeaker: Houcine Ben Dali\, Harvard CMSA \nTitle: A combinatorial formula for interpolation Macdonald polynomials \nAbstract: In 1996\, Knop and Sahi introduced a remarkable family of inhomogeneous symmetric polynomials\, defined via vanishing conditions\, whose top homogeneous parts are exactly the Macdonald polynomials. Like the Macdonald polynomials\, these interpolation Macdonald polynomials are closely connected to the Hecke algebra\, and admit nonsymmetric versions\, which generalize the nonsymmetric Macdonald polynomials. I will present a combinatorial formula for interpolation Macdonald polynomials in terms of signed multiline queues. This formula generalizes the combinatorial formula for Macdonald polynomials in terms of multiline queues given by Corteel–Mandelshtam–Williams. This is based on a joint work with Lauren Williams.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-12525/
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-12.5.25.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251208T150000
DTEND;TZID=America/New_York:20251208T160000
DTSTAMP:20260405T040128
CREATED:20251202T152832Z
LAST-MODIFIED:20251202T160431Z
UID:10003841-1765206000-1765209600@cmsa.fas.harvard.edu
SUMMARY:Computing WKB periods 
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Max Meynig\, University of Connecticut \nTitle: Computing WKB periods \nAbstract:  In one dimensional quantum mechanics\, the all-orders WKB method leads to ‘quantum periods’ which are formal power series in \hbar whose coefficients are certain period integrals. These periods\, which limelight in supersymmetric/string theories\, have rich structure and can be computed in a number of ways. I will discuss a new perspective on them and their computation.
URL:https://cmsa.fas.harvard.edu/event/qft_12825/
LOCATION:CMSA Room G02\, 20 Garden Street\, Cambridge\, MA\, 02138
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-12.8.25.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251208T163000
DTEND;TZID=America/New_York:20251208T173000
DTSTAMP:20260405T040128
CREATED:20251202T153625Z
LAST-MODIFIED:20251202T162404Z
UID:10003843-1765211400-1765215000@cmsa.fas.harvard.edu
SUMMARY:Recent Advances in Probabilistically Checkable Proofs
DESCRIPTION:Colloquium \nSpeaker: Dor Minzer (MIT) \nTitle: Recent Advances in Probabilistically Checkable Proofs \nAbstract: The PCP Theorem is a cornerstone of computer science\, with applications to hardness of approximation\, verification\, interactive protocols and more. It asserts a witness for the satisfiability of a given 3CNF formula can be encoded in a robust way that allows local checking.In this talk we discuss recent developments in PCPs\, and their connection with distributed protocols\, high-dimensional expanders and discrete Fourier analysis. Based on joint works with Kai Zhe Zheng\, Mitali Bafna\, Noam Lifshitz\, Nikhil Vyas.
URL:https://cmsa.fas.harvard.edu/event/colloquium-12825/
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-12.8.2025.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251209T161500
DTEND;TZID=America/New_York:20251209T183000
DTSTAMP:20260405T040128
CREATED:20251031T145823Z
LAST-MODIFIED:20251208T150959Z
UID:10003830-1765296900-1765305000@cmsa.fas.harvard.edu
SUMMARY:Geometry and Quantum Theory Seminar
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Lorenzo Riva\, CMSA \nTitle: Aganagic’s invariant is Khovanov homology \nAbstract: Webster computed the Khovanov homology of (the closure of) a braid in terms of the action of that braid on a certain KLRW category. Aganagic proposed that the same computation could be done in the Fukaya-Seidel category of the multiplicative Coulomb branch associated to a weighted quiver. In this talk we will recap the story so far and then sketch LePage and Shende’s proof of Aganagic’s proposal. \n  \nSpeaker: Bowen Yang\, CMSA \nTitle: Some groups from Condensed matter physics \nAbstract: I would like to talk about some groups coming from the study of quantum spin systems. They inspired a construction of generalized homology theories related to Azumaya algebras. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_12925/
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-12.9.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251210T120000
DTEND;TZID=America/New_York:20251210T130000
DTSTAMP:20260405T040128
CREATED:20251209T223200Z
LAST-MODIFIED:20251209T223544Z
UID:10003844-1765368000-1765371600@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Dan Freed\, CMSA
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Dan Freed\, CMSA \nTopic: Constructions of homotopy types in geometry and physics \n 
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_121025/
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-12.10.2025-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251211T140000
DTEND;TZID=America/New_York:20251211T150000
DTSTAMP:20260405T040128
CREATED:20251202T153632Z
LAST-MODIFIED:20251202T161106Z
UID:10003842-1765461600-1765465200@cmsa.fas.harvard.edu
SUMMARY:Covers of curves\, Ceresa cycles\, and unlikely intersections
DESCRIPTION:Algebra Seminar \nSpeaker: Padamavathi Srinivasan\, Boston University \nTitle: Covers of curves\, Ceresa cycles\, and unlikely intersections \nAbstract: The Ceresa cycle is a canonical homologically trivial algebraic cycle associated to a curve in its Jacobian. In his 1983 thesis\, Ceresa showed that this cycle is algebraically nontrivial for a very general complex curve of genus at least 3. In the last few years\, there have been many new results shedding light on the locus in the moduli space of genus g curves where the Ceresa cycle becomes torsion. We will survey these recent results and provide new examples of positive dimensional families of curves where only finitely many members of the family have torsion Ceresa cycle. The main idea is to study covers of curves with many automorphisms\, and we will explain how we use the covering maps together with results on unlikely intersections in abelian varieties to construct such families. This is joint work with Tejasi Bhatnagar\, Sheela Devadas and Toren D’Nelly Warady. \n 
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_121125/
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-12.11.25.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251215T163000
DTEND;TZID=America/New_York:20251215T173000
DTSTAMP:20260405T040128
CREATED:20251124T150428Z
LAST-MODIFIED:20251211T145044Z
UID:10003836-1765816200-1765819800@cmsa.fas.harvard.edu
SUMMARY:The active Young-Dupré equation
DESCRIPTION:Colloquium \nSpeaker: Julien Tailleur\, MIT \nTitle: The active Young-Dupré equation \nAbstract: The Young-Dupré equation is a cornerstone of the equilibrium theory of capillary and wetting phenomena. In the biological world\, interfacial phenomena are ubiquitous\, from the spreading of bacterial colonies to tissue growth and flocking of birds\, but the description of such active systems escapes the realm of equilibrium physics. I will show how a microscopic\, mechanical definition of surface tension allows building an Active Young-Dupré equation able to account for the partial wetting observed in simulations of active particles interacting via pairwise forces. Remarkably\, the equation shows that the corresponding steady interfaces do not result from a simple balance between the surface tensions at play but instead emerge from a complex feedback mechanism. The interfaces are indeed stabilized by a drag force due to the emergence of steady currents\, which are themselves a by-product of the symmetry breaking induced by the interfaces. These currents also lead to new physics by selecting the sizes and shapes of adsorbed droplets\, breaking the equilibrium scale-free nature of the problem. Finally\, I will demonstrate a spectacular consequence of the negative value of the liquid-gas surface tensions in systems undergoing motility-induced phase separation: partially-immersed objects are expelled from the liquid phase\, in stark contrast with what is observed in passive systems. These results lay the foundations for a theory of wetting in active systems.
URL:https://cmsa.fas.harvard.edu/event/colloquium-121525/
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-12.15.2025.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251216T140000
DTEND;TZID=America/New_York:20251216T150000
DTSTAMP:20260405T040128
CREATED:20251210T174651Z
LAST-MODIFIED:20251211T144851Z
UID:10003845-1765893600-1765897200@cmsa.fas.harvard.edu
SUMMARY:Electrical networks\, Grassmannians\, and cluster algebras
DESCRIPTION:Algebra Seminar \nSpeaker: Lazar Guterman\, Hebrew University of Jerusalem \nTitle: Electrical networks\, Grassmannians\, and cluster algebras \nAbstract: An electrical network with $n$ boundary vertices induces a matrix called the response matrix which measures the electrical properties of the network. The set of response matrices of all electrical networks has a characterization in terms of positivity of circular minors. Alman\, Lian and Tran constructed a cluster algebra on the set of circular minors\, which encodes the tests for positivity of these minors. Lam established the embedding of the set of electrical networks with $n$ boundary vertices into the totally nonnegative Grassmannian $Gr_{\ge0}(n-1\,2n)$. The coordinate ring of the Grassmannian has a cluster algebra structure as was proved by Scott. Given an electrical network\, we find a relation between circular minors of its response matrix and Plücker coordinates of its image in the Grassmannian. Using this property\, we prove that for an odd $n$ the two cluster algebras\, on circular minors and on the Grassmanian\, become isomorphic after a natural freezing and subsequent trivialization of certain variables in their initial seeds. We apply this isomorphism in order to relate the tests for positivity of circular minors to tests for positivity in the Grassmannian. The talk is based on a joint work with Boris Bychkov and Anton Kazakov. \n 
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_121625/
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-12.16.25.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251216T161500
DTEND;TZID=America/New_York:20251216T183000
DTSTAMP:20260405T040128
CREATED:20251031T150328Z
LAST-MODIFIED:20251031T150328Z
UID:10003824-1765901700-1765909800@cmsa.fas.harvard.edu
SUMMARY:Geometry and Quantum Theory Seminar
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: tba
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_121625/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, 02138
CATEGORIES:Geometry and Quantum Theory Seminar
END:VEVENT
END:VCALENDAR