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February | February | February | February | February | 1 - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: A new lower bound for sphere packing
Speaker: Julian Sahasrabudhe – Cambridge 3:00 PM-4:00 PM March 1, 2024 What is the maximum proportion of d-dimensional space that can be covered by disjoint, identical spheres? In this talk I will discuss a new lower bound for this problem, which is the first asymptotically growing improvement to Rogers’ bound from 1947. Our proof is almost entirely combinatorial and reduces to a novel theorem about independent sets in graphs with bounded degrees and codegrees. This is based on joint work with Marcelo Campos, Matthew Jenssen and Marcus Michelen. **Special Location** =============================== For more info, see https://math.mit.edu/combin/ - GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR: Gauge Theory and Topology Seminar: Sutured TQFTs and Floer homology
Speaker: Jake Rasmussen – University of Illinois Urbana-Champaign 3:30 PM-4:30 PM March 1, 2024 1 Oxford Street, Cambridge, MA 02138 USA
The bordered Floer homology of Lipshitz, Ozsvath, and Thurston was interpreted by Auroux as defining an element in the partially wrapped Fukaya category of a symmetric product of the boundary. We naturally expect that this assignment should be functorial; e.g. a cobordism between two manifolds with torus boundary should induce a morphism between the corresponding Lagrangians. I’ll describe a framework for thinking about functoriality in terms of sutured manifolds and describe what it looks like for Heegaard Floer homology.
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3 | 4 - CMSA EVENT: CMSA Colloquium: Strong bounds for arithmetic progressions
Speaker: Raghu Meka – UCLA 4:30 PM-5:30 PM March 4, 2024 20 Garden Street, Cambridge, MA 02138 Suppose you have a set S of integers from {1,2,…,N} that contains at least N / C elements. Then for large enough N, must S contain three equally spaced numbers (i.e., a 3-term arithmetic progression)? In 1953, Roth showed this is the case when C is roughly (log log N). Behrend in 1946 showed that C can be at most exp(sqrt(log N)). Since then, the problem has been a cornerstone of the area of additive combinatorics. Following a series of remarkable results, a celebrated paper from 2020 due to Bloom and Sisask improved the lower bound on C to C = (log N)^(1+c) for some constant c > 0. This talk will describe a new work showing that C can be much closer to Behrend’s construction. Based on joint work with Zander Kelley.
| 5 - CMSA EVENT: CMSA General Relativity Seminar: High order WENO finite difference scheme for Einstein-Yang-Mills equations
Speaker: Yuewen Chen – Tsinghua University 11:00 AM-12:00 PM March 5, 2024 In this talk, we will show the convergence analysis of the first-order finite difference scheme for static spherically symmetric $SU(2)$ Einstein-Yang-Mills (EYM) equations. We also construct a new WENO scheme for EYM.
Zoom: https://harvard.zoom.us/j/7855806609 Password: cmsa - CMSA EVENT: CMSA General Relativity Seminar: High order WENO finite difference scheme for Einstein-Yang-Mills equations
Speaker: Yuewen Chen – Tsinghua University 11:00 AM-12:00 PM March 5, 2024 In this talk, we will show the convergence analysis of the first-order finite difference scheme for static spherically symmetric $SU(2)$ Einstein-Yang-Mills (EYM) equations. We also construct a new WENO scheme for EYM.
Zoom: https://harvard.zoom.us/j/7855806609 Password: cmsa - RANDOM MATRIX SEMINAR: Probability Seminar: The Busemann process of (1+1)-dimensional directed polymers
Speaker: Erik Bates – North Carolina State University 1:30 PM-2:30 PM March 5, 2024 Directed polymers are a statistical mechanics model for random growth. Their partition functions are solutions to a discrete stochastic heat equation. This talk will discuss the logarithmic derivatives of the partition functions, which are solutions to a discrete stochastic Burgers equation. Of interest is the success or failure of the “one force-one solution principle” for this equation. I will reframe this question in the language of polymers, and share some surprising results that follow. Based on joint work with Louis Fan and Timo Seppäläinen. - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: On the canonical bundle formula in positive characteristic
Speaker: Marta Benozzo – Imperial College 3:00 PM-4:00 PM March 5, 2024 1 Oxford Street, Cambridge, MA 02138 USA An important problem in birational geometry is trying to relate in a meaningful way the canonical bundles of the source and the base of a fibration. The first instance of such a formula is Kodaira’s canonical bundle formula for surfaces which admit a fibration with elliptic fibres. It describes the relation between the canonical bundles in terms of the singularities of the fibres and their j-invariants. In higher dimension, we do not have an equivalent of the j-invariant, but we can still define a moduli part. Over fields of characteristic 0, positivity properties of the moduli part have been studied using variations of Hodge structures. Recently, the problem has been approached with techniques from the minimal model program. These methods can be used to prove a canonical bundle formula result in positive characteristic. For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar
| 6 - CMSA EVENT: CMSA New Technologies in Mathematics Seminar: LILO: Learning Interpretable Libraries by Compressing and Documenting Code
Speaker: Gabriel Grand – MIT CSAIL and Dept. of EE&CS 2:00 PM-3:00 PM March 6, 2024 20 Garden Street, Cambridge, MA 02138 While large language models (LLMs) now excel at code generation, a key aspect of software development is the art of refactoring: consolidating code into libraries of reusable and readable programs. In this paper, we introduce LILO, a neurosymbolic framework that iteratively synthesizes, compresses, and documents code to build libraries tailored to particular problem domains. LILO combines LLM-guided program synthesis with recent algorithmic advances in automated refactoring from Stitch: a symbolic compression system that efficiently identifies optimal lambda abstractions across large code corpora. To make these abstractions interpretable, we introduce an auto-documentation (AutoDoc) procedure that infers natural language names and docstrings based on contextual examples of usage. In addition to improving human readability, we find that AutoDoc boosts performance by helping LILO’s synthesizer to interpret and deploy learned abstractions. We evaluate LILO on three inductive program synthesis benchmarks for string editing, scene reasoning, and graphics composition. Compared to existing neural and symbolic methods – including the state-of-the-art library learning algorithm DreamCoder – LILO solves more complex tasks and learns richer libraries that are grounded in linguistic knowledge.
https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09 Password: cmsa - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Permutohedral complexes and curves with cyclic action
Speaker: Emily Clader – SFSU 4:15 PM-5:15 PM March 6, 2024 There is a beautiful story connecting the permutohedron to several different objects in algebra, geometry, and combinatorics: namely, to the symmetric group, to the geometry of a particular moduli space of curves, and to the theory of matroids. Somewhat more recently, the analogue of this story in type B was developed, where the role of the permutohedron is played by the signed permutohedron and the corresponding moduli space parameterizes curves with an involution. I will discuss joint work with C. Damiolini, C. Eur, D. Huang, S. Li, and R. Ramadas that develops a further generalization, defining a “permutohedral complex” that relates to a certain family of complex reflection groups, to the geometry of a moduli space of curves with finite-order automorphism, and to the combinatorics of multimatroid =============================== For more info, see https://math.mit.edu/combin/
| 7 - CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: Geometric construction of toric NCRs
Speaker: Jesse Huang – University of Alberta 10:30 AM-11:30 AM March 7, 2024 20 Garden Street, Cambridge, MA 02138 The Rouquier dimension of a toric variety is recently shown to be achieved by the Frobenius pushforward of O via coherent-constructible correspondence. From the perspective of noncommutative geometry, this result leads to a geometric construction of toric NCR of the invariant ring of the Cox ring with respect to a multi-grading which also gives the information about its global dimension. From the perspective of mirror symmetry, the same construction provides a universal “wall skeleton” capturing VGIT wall-crossings, which contains a window for each chamber as a full subcategory. From the perspective of commutative algebra, the same construction indicates the existence of virtual resolutions of the multigraded diagonal bimodule, which agrees with a recent result of Hanlon-Hicks-Larzarev constructing one such resolution explicitly. In this talk, I will survey these perspectives. The talk is based on joint works with P. Zhou, joint works with D. Favero, and work in progress with D. Favero. Zoom: https://harvard.zoom.us/j/93338480366?pwd=NEROWElhWStQVjVLRVZFSm1tV1ZCdz09 Passcode: 564263
| 8 - CMSA EVENT: CMSA Member Seminar: Symmetry in quantum field theory
Speaker: Dan Freed – Harvard University 12:00 PM-1:00 PM March 8, 2024
In joint work with Greg Moore and Constantin Teleman we show how ideas and techniques in topological field theory apply to the study of symmetry in quantum field theory. I will discuss how this came about, beginning with some discussion of symmetry in mathematics more generally, and give some examples.
Friday, March 8 at 12pm, with lunch, in the lounge at CMSA (20 Garden Street). Also by Zoom: https://harvard.zoom.us/j/92410768363 - CMSA EVENT: CMSA Member Seminar: Symmetry in quantum field theory
Speaker: Dan Freed – Harvard University 12:00 PM-1:00 PM March 8, 2024
In joint work with Greg Moore and Constantin Teleman we show how ideas and techniques in topological field theory apply to the study of symmetry in quantum field theory. I will discuss how this came about, beginning with some discussion of symmetry in mathematics more generally, and give some examples.
Friday, March 8 at 12pm, with lunch, in the lounge at CMSA (20 Garden Street). Also by Zoom: https://harvard.zoom.us/j/92410768363 - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Nilsequences on general additive patterns
Speaker: Daniel Altman – University of Michigan 3:00 PM-4:00 PM March 8, 2024
We will begin by briefly introducing the use of higher-order Fourier analysis in additive combinatorics for a general audience. In particular, we will discuss the arithmetic regularity lemma and how it identifies a certain class of arithmetically-structured functions — nilsequences — as extremal objects for problems in additive combinatorics. We will then discuss how it has recently come to light that the analysis of nilsequences on certain additive patterns — those which satisfy a certain algebraic criterion known as the flag condition — is easier than the general case, and discuss some recent ideas and developments in overcoming the difficulties that arise when the additive pattern of interest is not flag. =============================== For more info, see https://math.mit.edu/combin/ - GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR: Gauge Theory and Topology Seminar: Calabi-Yau monopoles, special Lagrangians, and Fueter sections
Speaker: Saman Habibi Esfahani – Duke University 3:30 PM-4:30 PM March 8, 2024 1 Oxford Street, Cambridge, MA 02138 USA
This talk investigates two types of proposed invariants of Calabi-Yau 3-folds: - from gauge theory: Calabi-Yau monopoles,
- from calibrated geometry: count of special Lagrangians weighted with their Fueter sections.
Here, we focus on three conjectures central to the definition of these invariants and their relations: - The Donaldson-Segal conjecture on gauge theory/calibrated geometry duality: Calabi-Yau monopoles = weighted count of special Lagrangians,
- The Donaldson-Scaduto conjecture: the existence of the pair of pants special Lagrangians, related to the formation of special Lagrangian singularities,
- A hyperkähler variation of the Atiyah-Floer conjecture for Fueter sections: monopole Fueter Floer homology = Lagrangian Fueter Floer homology.
The discussion explores recent progress on these conjectures. This is joint work with Yang Li.
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10 | 11 | 12 - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: The defect of a cubic fourfold
Speaker: Lisa Marquand – New York University 3:00 PM-4:00 PM March 12, 2024 1 Oxford Street, Cambridge, MA 02138 USA The defect of a cubic threefold with isolated singularities is a measure of the failure of Poincare duality, and also the failure to be Q-factorial. From the work of Cheltsov, a cubic threefold with only nodal singularities is Q factorial if and only if there are at most 5 nodes. We investigate the defect of cubic threefolds with worse than nodal isolated singularities, and provide a geometric method to compute this global invariant. One can then compute the Mixed Hodge structure on the middle cohomology of the cubic threefold, in terms of the defect (a global invariant) and local invariants (Du Bois and Link invariants) determined by the singularity types. We then relate the defect to geometric properties of the cubic threefold, showing it is positive if and only if the cubic contains a plane or a rational normal cubic scroll. The focus of this work is to provide more insight into the existence of reducible fibers for compactified intermediate jacobian fibrations associated to a smooth (not necessarily general) cubic fourfold. This is joint work with Sasha Viktorova. For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar
| 13 | 14 | 15 - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Hypergraph embeddings and decompositions: robustness via spreadness
Speaker: Tom Kelly – Georgia Tech 3:00 PM-4:00 PM March 15, 2024 A graph H embeds in a graph G if G contains a subgraph isomorphic to H, and it decomposes G if the edges of G can be partitioned into subgraphs isomorphic to H. Questions about when a graph embeds in or decomposes another are central in combinatorics. “Dirac-type” embedding results address minimum-degree conditions to ensure an embedding of some graph. Block designs, a fundamental object of Design Theory, are decompositions of complete graphs. In this talk, we will discuss robustness of embeddings and decompositions. For example, given a hypergraph of large minimum degree, we will discuss the threshold for a random subhypergraph to have a perfect matching or Hamilton cycle. We will also discuss the threshold for constructing block designs using only a random selection of blocks. All of these results utilize the recent Park–Pham Theorem or one of its variants. A crucial notion for this is that of the spreadness of a certain type of probability distribution. =============================== For more info, see https://math.mit.edu/combin/
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17 | 18 - CMSA EVENT: CMSA Colloquium: Koszul duality & twisted holography for asymptotically flat spacetimes
Speaker: Natalie Paquette – University of Washington Seattle 4:30 PM-5:30 PM March 18, 2024 20 Garden Street, Cambridge, MA 02138
Koszul duality has been understood in recent years to characterize order-type defects in twists of supersymmetric field theories. This notion has been generalized, from a physical point of view, by studying couplings between D-branes and closed string theories in the topological string. Computing the D-brane backreaction, and studying the resulting open/closed string duality, is the purview of the twisted holography program. Twisted holography seeks to study supersymmetric sectors of the AdS/CFT correspondence using these methods, and leverage the appropriate generalization of Koszul duality to elucidate the bulk/boundary map. When applying these methods to a topological string configuration on twistor space, one can construct an instance of twisted holography in which a 2d chiral algebra, supported on the “celestial sphere”, is dual to a 4d theory in an asymptotically flat spacetime. This is the first such top-down example of holography in a 4d asymptotically flat spacetime. This talk describes joint work done, variously, with Kevin Costello, Brian Williams, and Atul Sharma. - CMSA EVENT: CMSA Colloquium: Koszul duality & twisted holography for asymptotically flat spacetimes
Speaker: Natalie Paquette – University of Washington Seattle 4:30 PM-5:30 PM March 18, 2024 20 Garden Street, Cambridge, MA 02138
Koszul duality has been understood in recent years to characterize order-type defects in twists of supersymmetric field theories. This notion has been generalized, from a physical point of view, by studying couplings between D-branes and closed string theories in the topological string. Computing the D-brane backreaction, and studying the resulting open/closed string duality, is the purview of the twisted holography program. Twisted holography seeks to study supersymmetric sectors of the AdS/CFT correspondence using these methods, and leverage the appropriate generalization of Koszul duality to elucidate the bulk/boundary map. When applying these methods to a topological string configuration on twistor space, one can construct an instance of twisted holography in which a 2d chiral algebra, supported on the “celestial sphere”, is dual to a 4d theory in an asymptotically flat spacetime. This is the first such top-down example of holography in a 4d asymptotically flat spacetime. This talk describes joint work done, variously, with Kevin Costello, Brian Williams, and Atul Sharma.
| 19 - SEMINARS: Probability Seminar: Bipartite spherical spin glass at critical temperature (with a random matrix detour)
Speaker: Elizabeth Collins-Woodfin – McGill University 1:30 PM-2:30 PM March 19, 2024 One of the fascinating phenomena of spin glasses is the dramatic change in behavior that occurs between the high and low temperature regimes. The free energy of the spherical Sherrington-Kirkpatrick (SSK) model, for example, has Gaussian fluctuations at high temperature, but Tracy-Widom fluctuations at low temperature. A similar phenomenon holds for the bipartite SSK model, and we show that, when the temperature is within a small window around the critical temperature, the free energy fluctuations converge to an independent sum of Gaussian and Tracy-Widom random variables (joint work with Han Le). Our work follows two recent papers that proved similar results for the SSK model (by Landon and by Johnstone, Klochkov, Onatski, Pavlyshyn). Analyzing bipartite SSK at critical temperature requires a variety of tools including classical random matrix results, contour integral techniques, and a CLT for the log-characteristic polynomial of Laguerre (Wishart) random matrices evaluated near the spectral edge. This last ingredient was not present in the literature when we began our project, so I will discuss our proof of this CLT, which has other applications separate from bipartite spin glasses. This seminar will take place on Zoom. Zoom link: https://harvard.zoom.us/j/98500892109 - SEMINARS: Probability Seminar: Elizabeth Collins-Woodfin, McGill
Speaker: Elizabeth Collins-Woodfin – McGill 1:30 PM-2:30 PM March 19, 2024 - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: Extending the torelli map to alternative compactifications of the moduli space of curves
Speaker: Changho Han – University of Waterloo 3:00 PM-4:00 PM March 19, 2024 1 Oxford Street, Cambridge, MA 02138 USA It is well-known that the Torelli map, that turns a smooth curve of genus g into its Jacobian (a principally polarized abelian variety of dimension g), extends to a map from the Deligne—Mumford moduli of stable curves to the moduli of semi-abelic varieties by Alexeev. Moreover, it is also known that the Torelli map does not extend over the alternative compactifications of the moduli of curves as described by the Hassett—Keel program, including the moduli of pseudostable curves (can have nodes and cusps but not elliptic tails). But it is not yet known whether the Torelli map extends over alternative compactifications of the moduli of curves described by Smyth; what about the moduli of curves of genus g with rational m-fold singularities, where m is a positive integer bounded above? As a joint work in progress with Jesse Kass and Matthew Satriano, I will describe moduli spaces of curves with m-fold singularities (with topological constraints) and describe how far the Torelli map extends over such spaces into the Alexeev compactifications. For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar - SEMINARS: Introductory Math Seminar: Can biocalculus help fix the calculus image problem?
Speaker: Carrie Diaz Eaton – Bates 3:00 PM-5:00 PM March 19, 2024 Calculus has an image problem in the biology major. Students are anxious about taking it, due to prior personal experience and because calculus as a major gateway course contributes significantly to attrition in biology. Biology instructors are not seeing the desired gains in problem solving and graphical interpretation important for their courses. This is exacerbated by increasing interest in big data and computational skills rather than the proofs and algebraic techniques methods which have traditionally played a dominant role in calculus. “Biocalculus,” on the other hand, is a promising remedy for these issues. Students in biocalculus articulate more detailed connections to the theory of their disciplines, have increased retention, and much higher learning gains. Biocalculus leverages students’ passion and knowledge about biology and data in ways that may be particularly important to repaying educational debts to students with identities marginalized in STEM. However, significant challenges remain, particularly professional development and other investment needed to support such interdisciplinary courses and the epistemological consequences of the shift required.
| 20 - CMSA EVENT: CMSA New Technologies in Mathematics Seminar: Solving olympiad geometry without human demonstrations
Speaker: Trieu H. Trinh – Google Deepmind and NYU Dept. of Computer Science 2:00 PM-3:00 PM March 20, 2024 Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning, owing to their reputed difficulty among the world’s best talents in pre-university mathematics. Current machine-learning approaches, however, are not applicable to most mathematical domains owing to the high cost of translating human proofs into machine-verifiable format. The problem is even worse for geometry because of its unique translation challenges, resulting in severe scarcity of training data. We propose AlphaGeometry, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstrations by synthesizing millions of theorems and proofs across different levels of complexity. AlphaGeometry is a neuro-symbolic system that uses a neural language model, trained from scratch on our large-scale synthetic data, to guide a symbolic deduction engine through infinite branching points in challenging problems. On a test set of 30 latest olympiad-level problems, AlphaGeometry solves 25, outperforming the previous best method that only solves ten problems and approaching the performance of an average International Mathematical Olympiad (IMO) gold medallist. Notably, AlphaGeometry produces human-readable proofs, solves all geometry problems in the IMO 2000 and 2015 under human expert evaluation and discovers a generalized version of a translated IMO theorem in 2004. https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09 Password: cmsa - COLLOQUIUMS: Special Colloquium: Stable degenerations of singularities
Speaker: Ziquan Zhuang – Johns Hopkins University 3:00 PM-4:00 PM March 20, 2024 1 Oxford Street, Cambridge, MA 02138 USA
Around 10 years ago, Donaldson and Sun discovered that metric limits of Ricci positive Kähler–Einstein manifolds are algebraic varieties, and their metric tangent cones also underlie some algebraic structure. I will talk about a general algebraic geometry theory behind this phenomenon. In particular, I will survey the recent solution of Li-Xu’s Stable Degeneration Conjecture, which predicts that every mild singularity on a complex algebraic variety has a canonical degeneration that shares many features of the metric tangent cones.
Talk at 3 pm in Science Center 507; Tea at 4 pm in the Math Common Room - NUMBER THEORY SEMINAR: CANCELED Number Theory Seminar: Jit Wu Yap (Harvard University)
Speaker: Jit Wu Yap – Harvard 3:00 PM-4:00 PM March 20, 2024 1 Oxford Street, Cambridge, MA 02138 USA CANCELED. Event to be rescheduled. For more info, see https://ashvin-swaminathan.github.io/home/NTSeminar.html - SEMINARS: Dynamics, Geometry and Moduli Spaces Seminar: Clusters algebras and Teichmueller theory
Speaker: Amanda Burcroff – Harvard 4:00 PM-5:00 PM March 20, 2024 See webpage for more details: https://people.math.harvard.edu/~ctm/sem/ - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Rational Catalan Numbers for Complex Reflection Groups
Speaker: Weston Miller – UT Dallas 4:15 PM-5:15 PM March 20, 2024 The spetsial complex reflection groups are complex reflection groups that behave as if they were the Weyl group for some connected reductive algebraic group. Analogs of unipotent characters and Lusztig’s Fourier transform can be defined combinatorially for these groups, allowing some techniques from the representation theory of finite groups of Lie type to be extended to spetsial complex reflection groups. In a recent paper, Galashin, Lam, Trinh, and Williams introduced a family of rational noncrossing objects for finite Coxeter groups. The proof that these objects are counted by rational Coxeter-Catalan numbers used Hecke algebra traces to compute the point count of braid Richardson varieties. Assuming standard conjectures, I prove that this trace technique extends to irreducible spetsial complex reflection groups. That is, I show that the trace of a power of a Coxeter element still produces a rational Catalan number. I’ll also discuss the related rational parking problem. =============================== For more info, see https://math.mit.edu/combin/
| 21 - CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: The KSBA moduli space of log Calabi-Yau surfaces
Speaker: Pierrick Bousseau – University of Georgia 10:30 AM-11:30 AM March 21, 2024 20 Garden Street, Cambridge, MA 02138
The KSBA moduli space, introduced by Kollár–Shepherd-Barron, and Alexeev, is a natural generalization of “the moduli space of stable curves” to higher dimensions. It parametrizes stable pairs (X,B), where X is a projective algebraic variety satisfying certain conditions and B is a divisor such that K_X+B is ample. This moduli space is described concretely only in a handful of situations: for instance, if X is a toric variety and B=D+\epsilon C, where D is the toric boundary divisor and C is an ample divisor, it is shown by Alexeev that the KSBA moduli space is a toric variety. Generally, for a log Calabi-Yau variety (X,D) consisting of a projective variety X and an anticanonical divisor D, with B=D+\epsilon C where C is an ample divisor, it was conjectured by Hacking–Keel–Yu that the KSBA moduli space is still toric (up to passing to a finite cover). In joint work with Alexeev and Argüz, we prove this conjecture for all log Calabi-Yau surfaces. This uses tools from the minimal model program, log smooth deformation theory and mirror symmetry. - CMSA EVENT: CMSA Active Matter Seminar: Decoding The Origins of Fluidity in Multicellular Systems
Speaker: Max Bi – Northeastern University 1:00 PM-2:00 PM March 21, 2024 20 Garden Street, Cambridge, MA 02138 Organisms continually adapt to mechanical forces at the cellular and tissue levels, a process crucial for sustaining vital life functions. In pivotal physiological processes, such as cancer progression and embryonic development, tissues are often poised near solid-like and fluid-like states. My talk will delve into three critical aspects of this phenomenon: (1) utilizing computational models that draw parallels with soft matter physics, we examine shear-induced rigidity and the origins of fluidity in epithelial tissues; (2) exploring the intricate relationship between external mechanical stresses and internal cellular dynamics, unraveling a range of rheological behaviors, such as shear thinning and thickening, which are key for understanding rheological responses in varying physical contexts; and (3) investigating how cellular processes like division and apoptosis influence tissue states, with a specific focus on the emergence of hexatic phases, an intermediate state exhibiting properties of both solids and liquids.
This seminar will be held in person and on Zoom. https://harvard.zoom.us/j/96657833341 Password: cmsa - THURSDAY SEMINAR SEMINAR: Thursday Seminar: Bounded cyclotomic spectra
Speaker: Jeremy Hahn – Harvard 3:30 PM-5:30 PM March 21, 2024 1 Oxford Street, Cambridge, MA 02138 USA I will discuss properties of a cyclotomic spectrum THH(R) that make the telescopic homotopy theory of TC(R) particularly computable, establish these properties in some cases, and begin to discuss their interactions with unipotent group actions.
| 22 - CMSA EVENT: CMSA Member Seminar: Modularity and Fibrations in Mirror Symmetry
Speaker: Chuck Doran – Bard College, University of Alberta, and Harvard CMSA 12:00 PM-1:00 PM March 22, 2024
We will introduce appearances of modularity in the study both of families of Calabi-Yau threefolds and of their enumerative invariants. An important role is played by the structure of fibrations and the DHT fibration-degeneration mirror correspondence, which clarifies how these notions of modularity are (and are not) related. This is joint work with Boris Pioline and Thorsten Schimannek.
Friday, March 22nd at 12pm, with lunch, lounge at CMSA (20 Garden Street). Also by Zoom: https://harvard.zoom.us/j/92410768363 - GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR: Gauge Theory and Topology Seminar: Slope detection, toroidal 3-manifolds, and the L-space conjecture
Speaker: Cameron Gordon – University of Texas at Austin 3:30 PM-4:30 PM March 22, 2024 1 Oxford Street, Cambridge, MA 02138 USA
We will describe an approach to the L-space conjecture for toroidal 3-manifolds based on notions of slope detection corresponding to the three properties in the conjecture. We will give some applications to toroidal manifolds with small first homology, cyclic branched covers of satellite links, and Dehn surgeries on satellite knots. This is joint work with Steve Boyer and Ying Hu. - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: A Tropical Edrei theorem
Speaker: Konstanze Rietsch – King’s College London 4:15 PM-5:15 PM March 22, 2024 The classical Edrei theorem from the 1950’s gives a parametrisation for infinite upper-triangular totally positive real Toeplitz matrices by pairs of sequences of positive real parameters with finite sum. These infinite matrices (and their parameters) are central for understanding characters of the infinite symmetric group, as was discovered by Thoma, who reproved Edrei’s theorem in the 1960’s. There is also a totally different (totally positive) theorem about Toeplitz matrices that relates to quantum cohomology of flag varieties and mirror symmetry [R,06]. Namely, this theorem provides an (inverse) parametrization in terms of ‘quantum parameters’ for the finite Toeplitz matrix case. This talk will be about new tropical versions of these parametrisation results. Toeplitz matrices in the tropical world turn out to have a nice combinatorial description. We also uncover a surprising relationship between the classical Edrei parameters and the quantum parameters of quantum cohomology. This work builds on results of Judd and Ludenbach and relates also to Lusztig’s parametrisation of his canonical basis. =============================== For more info, see https://math.mit.edu/combin/
| 23 - CONFERENCE: Mahindra Humanities Center Interdisciplinary Graduate Student Conference: Unfiguring – Illustrating Infinity
Speaker: Curtis T. McMullen – Harvard Mathematics 1:40 PM-2:45 PM March 23, 2024 Barker Ctr, 12 Quincy St, Cambridge, MA 02138 Curtis T. McMullen, Cabot Professor of Mathematics at Harvard, will give keynote talk on “Illustrating Infinity” as a part of Unfiguring, the Mahindra Humanities Center Interdisciplinary Graduate Student Conference. This talk will be on Saturday, 23 March, 1:45pm in the Thompson room of the Barker Center. If you wish to attend, please see the link below to register for the event. Unfiguring will take place in person in Cambridge, MA from March 21–23, 2024. There will be a performance and reception for this even in the SC ground floor on Thursday at 6pm. See the schedule here. To attend, register here. A separate registration is required for each day of the conference. Lunch will be provided on Friday and Saturday. For more information on this event, please see the Unfiguring webpage.
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24 | 25 - CMSA EVENT: Arithmetic Quantum Field Theory Conference
9:00 AM-5:00 PM March 25, 2024-March 29, 2024 20 Garden Street, Cambridge, MA 02138 Arithmetic Quantum Field Theory Conference Dates: March 25–29, 2024 Location: Room G10, Harvard CMSA, 20 Garden Street, Cambridge MA 02138 Directions and Recommended Lodging Speakers and schedule TBA. Organizers: - COLLOQUIUMS: Special Colloquium: The arithmetic of some Dirichlet L-values
Speaker: Frank Calegari – University of Chicago 3:00 PM-4:00 PM March 25, 2024 1 Oxford Street, Cambridge, MA 02138 USA
Starting with the “Leibniz” formula for π π/4 = 1 – 1/3 + 1/5 – 1/7 + … the special values of Dirichlet L-functions have long been a source of fascination and frustration. From Euler’s solution in 1734 of the Basel problem to Apery’s proof in 1978 that zeta(3) is irrational, our progress on understanding the arithmetic of these numbers has been limited. In this talk, we discuss some results (old and new) about these numbers.
Talk at 3 pm in Science Center 507; Tea at 4 pm in the Math Common Room
| 26 - CMSA EVENT: Arithmetic Quantum Field Theory Conference
9:00 AM-5:00 PM March 26, 2024-March 29, 2024 20 Garden Street, Cambridge, MA 02138 Arithmetic Quantum Field Theory Conference Dates: March 25–29, 2024 Location: Room G10, Harvard CMSA, 20 Garden Street, Cambridge MA 02138 Directions and Recommended Lodging Speakers and schedule TBA. Organizers: - SEMINARS: Probability Seminar: Global well-posedness of the stochastic Abelian-Higgs equations in two dimensions
Speaker: Sky Cao – MIT 1:30 PM-3:00 PM March 26, 2024
There has been much recent progress on the local solution theory for geometric singular SPDEs. However, the global theory is still open in most cases. My talk will be about global well-posedness for the 2D stochastic Abelian-Higgs model, which is a geometric singular SPDE arising from gauge theory. The proof is based on a new covariant (i.e. geometric) approach, which consists of two parts: (1) introducing covariant stochastic objects (2) controlling nonlinear remainders using a covariant monotonicity formula, which is inspired by earlier work of Hamilton. This is joint work with Bjoern Bringmann. - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: A degeneration of the Hilbert scheme
Speaker: Dhruv Ranganathan – Cambridge 3:00 PM-4:00 PM March 26, 2024 Grothendieck’s Hilbert scheme is a compact parameter space for subschemes of a projective scheme X. It is one of the basic moduli spaces in algebraic geometry, in the sense that it is the starting point for the construction of many others. One simple question about the Hilbert scheme is the following: as X undergoes a nice degeneration, what is the right way to degenerate the Hilbert scheme of X along with it? One possible answer, proposed in the PhD thesis of Kennedy-Hunt, comes from an object called the logarithmic Hilbert scheme. I will give an introduction to this circle of these ideas, explain the basic geometric properties of the logarithmic Hilbert scheme, and sketch connections with certain moduli spaces of higher dimensional varieties. The talk reports on work of Kennedy-Hunt, joint work with Kennedy-Hunt, and joint work with Maulik. For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar - SEMINARS: Mathematical Picture Language Seminar: Certifying Almost All Quantum States with Few Single-qubit Measurements
Speaker: Robert Huang – California Institute of Technology 4:30 PM-5:30 PM March 26, 2024
Quantum systems can exhibit highly complex entanglement. Certifying that an n-qubit state in the experimental lab is close to a highly-entangled target state typically requires deep entangling circuits or exponentially many single-qubit measurements. In this work, we prove that almost all n-qubit target states, including those with exponential circuit complexity, can be certified from only O(n^2) single-qubit measurements. This result is established by a new technique relating certification to a random walk’s mixing time. Our protocol has applications for benchmarking the fidelity of quantum systems and for learning and verifying neural networks, tensor networks, and various other representations of quantum states using only single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties that would otherwise require an exponential number of measurements.
*In-person and on Zoom* QR Code & Link: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09 Passcode: 657361 https://mathpicture.fas.harvard.edu/seminar
| 27 - CMSA EVENT: Arithmetic Quantum Field Theory Conference
9:00 AM-5:00 PM March 27, 2024-March 29, 2024 20 Garden Street, Cambridge, MA 02138 Arithmetic Quantum Field Theory Conference Dates: March 25–29, 2024 Location: Room G10, Harvard CMSA, 20 Garden Street, Cambridge MA 02138 Directions and Recommended Lodging Speakers and schedule TBA. Organizers: - NUMBER THEORY SEMINAR: Number Theory Seminar: “everywhere unramified” objects in number theory and the cohomology of GLn(Z)
Speaker: Frank Calegari – University of Chicago 3:00 PM-4:00 PM March 27, 2024 1 Oxford Street, Cambridge, MA 02138 USA One theme in number theory is to study objects via their ramification: the discriminant of a number field, the conductor of an elliptic curve, the level of a modular form, and so on. There is, however, some particular interest in understanding objects which are “everywhere unramified” — and also understanding when such objects don’t exist. Such non-existence results are often the starting point for inductive arguments. For example, Minkowski’s theorem that there are no unramified extensions of Q can be used to prove the Kronecker-Weber theorem, and the vanishing of a certain space of modular forms is the starting point for Wiles’ proof of Fermat’s Last Theorem. In this talk, I will begin by describing many such vanishing results both in arithmetic and in the theory of automorphic forms, and how they are related by the Langlands program (sometimes only conjecturally). Then I will describe the construction of a new example of an automorphic form of level one and “weight zero”. This construction also gives the first non-zero classes in the cohomology of GLn(Z) (for some n) that come from “cuspidal” modular forms (for n > 0). For more info, see https://ashvin-swaminathan.github.io/home/NTSeminar.html - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Pecha Kucha
3:00 PM-4:00 PM March 27, 2024 There will be Pecha Kucha talks by: Alan Yan, Amanda Burcroff, Chris Eur, Colin Defant, Grant Barkley, Jiyang Gao, Jon Boretsky, Victor Wang, and Yuhan Jiang. =============================== For more info, see https://math.mit.edu/combin/ - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Positivity in real Schubert calculus
Speaker: Steven Karp – Notre Dame 4:15 PM-5:15 PM March 27, 2024 Schubert calculus involves studying intersection problems among linear subspaces of C^n. A classical example of a Schubert problem is to find all 2-dimensional subspaces of C^4 which intersect 4 given 2-dimensional subspaces nontrivially (it turns out there are 2 of them). In the 1990’s, B. and M. Shapiro conjectured that a certain family of Schubert problems has the remarkable property that all of its complex solutions are real. This conjecture inspired a lot of work in the area, including its proof by Mukhin-Tarasov-Varchenko in 2009. I will present a strengthening of this result which resolves some conjectures of Sottile, Eremenko, Mukhin-Tarasov, and myself, based on surprising connections with total positivity, the representation theory of symmetric groups, symmetric functions, and the KP hierarchy. This is joint work with Kevin Purbhoo. =============================== For more info, see https://math.mit.edu/combin/
| 28 - CMSA EVENT: Arithmetic Quantum Field Theory Conference
9:00 AM-5:00 PM March 28, 2024-March 29, 2024 20 Garden Street, Cambridge, MA 02138 Arithmetic Quantum Field Theory Conference Dates: March 25–29, 2024 Location: Room G10, Harvard CMSA, 20 Garden Street, Cambridge MA 02138 Directions and Recommended Lodging Speakers and schedule TBA. Organizers: - THURSDAY SEMINAR SEMINAR: Thursday Seminar: The THH of the cochains of the circle
Speaker: Ishan Levy – Harvard 3:30 PM-5:30 PM March 28, 2024 1 Oxford Street, Cambridge, MA 02138 USA We will study the THH of the fixed points of a ring spectrum by a trivial Z-action as a cyclotomic spectrum. In particular, we will see that the coassembly map for the trivial Z-action on T(n+1)-local TC of a ring spectrum R is never an isomorphism as long as the T(n+1)-local TC of R is nonzero. We will then explain how the disproof of the telescope conjecture follows from asymptotically comparing Adams operations to the trivial action. - CMSA EVENT: 2024 Ding Shum Lecture: Yann Lecun: Objective-Driven AI: Towards AI systems that can learn, remember, reason, and plan
Speaker: Yann LeCun – 4:30 PM-5:30 PM March 28, 2024 1 Oxford Street, Cambridge, MA 02138 On March 28, 2024, the CMSA will host the fifth annual Ding Shum Lecture, given by Yann LeCun. Time: 4:30–5:30 pm ET Location: Harvard Science Center Hall A & via Zoom Webinar Registration is required. Title: Objective-Driven AI: Towards AI systems that can learn, remember, reason, and plan Abstract: How could machines learn as efficiently as humans and animals? How could machines learn how the world works and acquire common sense? How could machines learn to reason and plan? Current AI architectures, such as Auto-Regressive Large Language Models fall short. I will propose a modular cognitive architecture that may constitute a path towards answering these questions. The centerpiece of the architecture is a predictive world model that allows the system to predict the consequences of its actions and to plan a sequence of actions that optimize a set of objectives. The objectives include guardrails that guarantee the system’s controllability and safety. The world model employs a Hierarchical Joint Embedding Predictive Architecture (H-JEPA) trained with self-supervised learning. The JEPA learns abstract representations of the percepts that are simultaneously maximally informative and maximally predictable. The corresponding working paper is available here: https://openreview.net/forum?id=BZ5a1r-kVsf
This event is made possible by the generous funding of Ding Lei and Harry Shum.
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