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1 | 2 - CMSA EVENT: Algebraic Geometry in String Theory Seminar: Motivic decomposition of moduli space from brane dynamics
Speaker: Kai Xu – CMSA 10:00 AM-11:30 AM October 2, 2023 20 Garden Street, Cambridge, MA 02138 Supersymmetric gauge theories encode deep structures in algebraic geometry, and geometric engineering gives a powerful way to understand the underlying structures by string/M theory. In this talk we will see how the dynamics of M5 branes tell us about the motivic and semiorthogonal decompositions of moduli of bundles on curves. Please note that there will be a pre-talk by Kai Xu from 10:00 am before the main talk at 10:30 - OTHER MATHEMATICS DEPARTMENT EVENTS: Jameel Al-Aidroos Mathematical Pedagogy Lecture Series
Speaker: Gregory R. Goldsmith – Schmid College of Science and Technology at Chapman University 3:00 PM-4:30 PM October 2, 2023 Join us for the second annual Jameel Al-Aidroos Mathematical Pedagogy Lecture Series When: October 2, 2023 | 3 p.m. – 4:30 p.m. Where: Science Center Room 507, 1 Oxford Street, Cambridge, MA, 02138 Speaker: Gregory R. Goldsmith - What does it mean to mentor?
- Every mentor is different. Every mentee is different.
Greg Goldsmith is the Associate Dean for Research and Development and an Associate Professor of Biological Sciences in the Schmid College of Science and Technology at Chapman University. He served for six years as the first director of the Grand Challenges Initiative, building it into one of the nation’s largest and most comprehensive postdoctoral training programs. REGISTER This speaker series is a small way to remember Jameel Al-Aidroos, his extraordinary warmth of character and pedagogical skills, and his contributions and dedication to teaching and learning at Harvard. He motivated and inspired his students and colleagues; through this series, we hope to celebrate and keep alive that legacy by bringing speakers who share new perspectives on mathematics and pedagogy, and motivate us to reflect on our professional roles. Organizers - Robin Gottlieb | Harvard Professor of the Practice in Teaching of Mathematics
- Brendan Kelly | Harvard Department of Mathematics Senior Preceptor, Director of Introductory Mathematics
- CMSA EVENT: CMSA Colloquium: Gravitational Instantons
Speaker: Yu-Shen Lin – Boston University 4:30 PM-5:30 PM October 2, 2023 20 Garden Street, Cambridge, MA 02138 Gravitational instantons were introduced by Hawking as building blocks of his Euclidean quantum gravity theory back in the 1970s. These are non-compact Calabi-Yau surfaces with L2 curvature and thus can be viewed as the non-compact analogue of K3 surfaces. K3 surfaces are 2-dimensional Calabi-Yau manifolds and are usually the testing stone before conquering the general Calabi-Yau problems. The moduli space of K3 surfaces and its compactification on their own form important problems in various branches in geometry. In this talk, we will discuss the Torelli theorem of gravitational instantons, how the cohomological invariants of a gravitational instanton determine them. As a consequence, this leads to a description of the moduli space of gravitational instantons.
| 3 - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: The Minimal Exponent of LCI Subvarieties
Speaker: Brad Dirks – Stony Brook 3:00 PM-4:00 PM October 3, 2023 1 Oxford Street, Cambridge, MA 02138 USA Classification of singularities is an interesting problem in many areas of algebraic geometry, like the minimal model program. One classical approach is to assign to a variety a rational number, its log canonical threshold. For complex hypersurface singularities, this invariant has been refined by M. Saito to the minimal exponent. This invariant is related to Bernstein-Sato polynomials, Hodge ideals and higher du Bois and higher rational singularities. In joint work with Qianyu Chen, Mircea Mustață and Sebastián Olano, we defined the minimal exponent for LCI subvarieties of smooth complex varieties. We relate it to local cohomology, higher du Bois and higher rational singularities. I will describe what was done in the hypersurface case, give our definition in the LCI case and explain the relation to local cohomology modules and the classification of singularities.
| 4 - NUMBER THEORY SEMINAR: Number Theory Seminar: Tate Classes and Endoscopy for GSp₄
Speaker: Naomi Sweeting – Harvard University 3:00 PM-4:00 PM October 4, 2023 1 Oxford Street, Cambridge, MA 02138 USA Weissauer proved using the theory of endoscopy that the Galois representations associated to classical modular forms of weight two appear in the middle cohomology of both a modular curve and a Siegel modular threefold. Correspondingly, there are large families of Tate classes on the product of these two Shimura varieties, and it is natural to ask whether one can construct algebraic cycles giving rise to these Tate classes. It turns out that a natural algebraic cycle generates some, but not all, of the Tate classes: to be precise, it generates exactly the Tate classes which are associated to generic members of the endoscopic L-packets on GSp₄. In the non-generic case, one can at least show that all the Tate classes arise from Hodge cycles. For this talk, I’ll focus on the behavior of the algebraic cycle class. NB: This talk is independent of the one in last week’s number theorists’ seminar. - SEMINARS: Informal Seminar on Dynamics, Geometry and Moduli Spaces: Automorphisms of complex surfaces: What is the simplest interesting dynamical system?
Speaker: C. McMullen – Harvard 4:00 PM-5:00 PM October 4, 2023 1 Oxford Street, Cambridge, MA 02138 USA Please see website for more details: www.math.harvard.edu/~ctm/sem. - OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood Seminar: Stack-Sorting and Beyond
Speaker: Colin Defant – Harvard University 4:30 PM-5:30 PM October 4, 2023 1 Oxford Street, Cambridge, MA 02138 USA
In 1990, West introduced the stack-sorting map, a combinatorially-defined operator on the set of permutations of size n that serves as a deterministic analogue of Knuth’s stack-sorting machine. I will discuss a method for computing the fertility of an arbitrary permutation, which is simply the number of preimages of the permutation under the stack-sorting map. This method uses combinatorial objects called valid hook configurations. Very surprisingly, valid hook configurations also appear in a formula that converts from free to classical cumulants in free probability theory. This allows us to use tools from free probability theory to prove deep facts about the stack-sorting map. On the other hand, we can also leverage the stack-sorting map to prove a new theorem that relates cumulants with special families of binary plane trees called troupes. This talk will be very elementary and combinatorial, and I will probably mention some open problems at the end. =============================== https://people.math.harvard.edu/~gammage/ons/
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8 | 9 | 10 - CMSA EVENT: CMSA General Relativity Seminar: Tidal Squeezing of Black Holes
Speaker: Maria Rodriguez – Utah 11:00 AM-12:00 PM October 10, 2023 20 Garden Street, Cambridge, MA 02138
Recent developments indicate that Kerr black holes do not deform when perturbed by a static external gravitational field. Relying on hidden symmetries, compelling progress has been achieved to explain that Love numbers for Kerr black holes vanish. How does the phenomenon of tidal squeezing manifest in broader contexts? An elementary presentation of dynamical tidal squeezing of Kerr black holes will be given.
Zoom: https://harvard.zoom.us/j/7855806609 Password: cmsa - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: Uniruling projective families over ℂℙ¹ with rational (multi)sections
Speaker: Alex Pieloch – MIT 3:00 PM-4:00 PM October 10, 2023 We will discuss a result which states that every projective family over ℂℙ¹ with at most two singular fibres is uniruled by rational (multi)sections. We obtain these rational curves by using techniques from symplectic geometry. In this talk, we will focus on (1) discussing the motivation for this work from Hodge theory and (2) presenting the geometric constructions and ideas involved in our proofs. No knowledge of symplectic geometry is required. Please note MIT location For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar - CMSA EVENT: CMSA Topological Quantum Matter Seminar: Chern Mosaic and ideal bands in helical trilayer graphene
Speaker: Daniele Guerci – Flatiron Institute 4:00 PM-5:00 PM October 10, 2023 20 Garden Street, Cambridge, MA 02138 In this talk I will present helical trilayer graphene (hTTG) which is characterized an emergent real-space Chern mosaic pattern resulting from the interface of two incommensurate moiré lattices [1]. This pattern shows distinct regions with finite integer Chern numbers separated by domain walls where the spectrum is gapless and connected at all energy scales [2]. After introducing the Hamiltonian describing hTTG I will focus my attention on the macroscopic domains, that host isolated flat bands with intriguing properties. Upon investigating the chiral limit, where analytical expressions can be derived, we found that the flat bands features the superposition of a Chern -1 and a Chern 2 bands described by the superposition of two lowest Landau level [2,3]. The origin of the flat bands can be explained using a combination of geometrical relations and symmetry arguments [3]. Building on this knowledge, I will discuss the properties of the zero-modes at higher magic angles. [1] Y.Mao,D.Guerci,C.Mora, PRB 107, 125423 (2023) [Editors’ Suggestion] [2] D.Guerci,Y.Mao,C.Mora, arXiv:2305.03702 (2023) [3] D.Guerci,Y.Mao,C.Mora, arXiv:2308.02638 (2023)
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/97514733653?pwd=Q05XN3oxSnYvaXlnS0dsRnVyMXZMUT09 Password: 353114
| 11 - CMSA EVENT: CMSA New Technologies in Mathematics Seminar: LeanDojo: Theorem Proving with Retrieval-Augmented Language Models
Speaker: Alex Gu – MIT Dept. of EE&CS 2:00 PM-3:00 PM October 11, 2023 20 Garden Street, Cambridge, MA 02138 Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. We introduce LeanDojo: an open-source Lean playground consisting of toolkits, data, models, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs, providing valuable data for premise selection: a key bottleneck in theorem proving. Using this data, we develop ReProver (Retrieval-Augmented Prover): the first LLM-based prover that is augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo’s program analysis capability to identify accessible premises and hard negative examples, which makes retrieval much more effective. Furthermore, we construct a new benchmark consisting of 96,962 theorems and proofs extracted from Lean’s math library. It features a challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09 - NUMBER THEORY SEMINAR: Number Theory Seminar: A relative Oda’s criterion
Speaker: Alex Betts – Harvard University 3:00 PM-4:00 PM October 11, 2023 1 Oxford Street, Cambridge, MA 02138 The Neron–Ogg–Shafarevich criterion asserts that an abelian variety over ℚp has good reduction if and only if the Galois action on its ℤℓ-linear Tate module is unramified (for ℓ different from p). In 1995, Oda formulated and proved an analogue of the Neron–Ogg–Shafarevich criterion for smooth projective curves X of genus at least two: X has good reduction if and only if the outer Galois action on its pro-ℓ geometric fundamental group is unramified. In this talk, I will explain a relative version of Oda’s criterion, due to myself and Netan Dogra, in which we answer the question of when the Galois action on the pro-ℓ torsor of paths between two points x and y is unramified in terms of the relative position of x and y on the reduction of X. On the way, we will touch on topics from mapping class groups and the theory of electrical circuits, and, time permitting, will outline some consequences for the Chabauty–Kim method. - SEMINARS: Informal Seminar on Dynamics, Geometry and Moduli Spaces: Islands on K3 surfaces
| 12 - CMSA EVENT: CMSA Active Matter Seminar: Contractility, structure formation and fluctuations in active gels, with and without molecular motors
Speaker: Fred MacKintosh – Rice University 1:00 PM-2:00 PM October 12, 2023 20 Garden Street, Cambridge, MA 02138 Various processes in living cells depend on contractile forces that are often generated by myosin motors in concert with polar actin filaments. A textbook example of this is the actomyosin contractile ring that forms during cell division. Recent evidence, however, has begun to suggest alternate or redundant mechanisms that do not depend on myosin. Experiments on simplified, reconstituted systems also point to contractility and structure formation in disordered, apolar arrays of filaments. We propose a motor-free mechanism that can generate contraction in biopolymer networks without the need for motors such as myosin or polar filaments such as actin. This mechanism is based on active binding and unbinding of cross-linkers that breaks the principle of detailed balance, together with the asymmetric force-extension response of semiflexible biopolymers. We discuss the resulting force-velocity relation and other implications of this, as well as possible evidence for non-motor force generation.
This seminar will be held in person and on Zoom. https://harvard.zoom.us/j/96657833341 Password: cmsa - SEMINARS: Thursday Seminar: Fun with defects (in topological quantum field theories)
Speaker: Dan Freed – Harvard 3:30 PM-5:30 PM October 12, 2023 1 Oxford Street, Cambridge, MA 02138 USA Thursday Seminar given by Dan Freed on “Fun with defects (in topological quantum field theories).”
| 13 - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Improved bounds for Heilbronn’s triangle problem and connections to projection theory
Speaker: Alex Cohen and Dmitrii Zakharov – MIT 3:00 PM-4:00 PM October 13, 2023
Heilbronn’s triangle problem asks, how small is the smallest triangle formed by a set of points? Suppose n points are placed in the unit square and Delta is the smallest area triangle formed by three of these points. It is not too hard to see that Delta < C n^{-1}. Komlos, Pintz, and Szemeredi proved in 1981 that Delta << C n^{-8/7} by building on an ingenious method of Roth. We improve the bound to Delta < C n^{-8/7-ep}. The improvement comes from establishing new connections between Heilbronn’s problem and projection theory. All joint with Cosmin Pohoata. =============================== For more info, see https://math.mit.edu/combin/ - GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR: Gauge Theory and Topology Seminar: On Freedman’s Link Packings
Speaker: Elia Portnoy – 3:30 PM-4:30 PM October 13, 2023 1 Oxford Street, Cambridge, MA 02138 USA
Freedman recently posed a new question in quantitative topology about link packings. Given a link L, define the $\epsilon$-diagonal packing number $n_{L(\epsilon)}$ to be the number of copies of L that can be simultaneously embedded in $[0,1]^3$ so that (1) Each copy of $L$ is contained in a ball which is disjoint from the other copies. (2) Within each copy, the components are separated by a distance of at least $\epsilon$. We’ll discuss a new construction for obtaining a lower bound on $n_{L(\epsilon)}$ and expand on Freedman’s ideas to obtain an upper bound on $n_{L(\epsilon)}$ when $L$ has a non-trivial Milnor Invariant. At the end we’ll mention several related open problems about link packings. This is joint work with Fedya Manin.
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15 | 16 - CMSA EVENT: Algebraic Geometry in String Theory Seminar: Moduli of boundary polarized Calabi-Yau pairs
Speaker: Dori Bejleri – CMSA 10:00 AM-11:30 AM October 16, 2023 20 Garden Street, Cambridge, MA 02138 The theories of KSBA stability and K-stability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to constructing a moduli space of Calabi-Yau pairs which should interpolate between KSBA and K-stable moduli via wall-crossing. I will explain how this approach can be used to construct projective moduli spaces of plane curve pairs. This is based on joint work with K. Ascher, H. Blum, K. DeVleming, G. Inchiostro, Y. Liu, X. Wang. Please note that there will be a pretalk by Rosie Shen (Harvard Math) from 10:00 am before the main talk at 10:30. The title of this pretalk is “Introduction to the singularities of the MMP.” - CMSA EVENT: CMSA Colloquium: An exploration of infinite games—infinite Wordle and the Mastermind numbers
Speaker: Joel D. Hamkins – Notre Dame and Oxford 4:30 PM-5:30 PM October 16, 2023 20 Garden Street, Cambridge, MA 02138 Let us explore the nature of strategic reasoning in infinite games, focusing on the cases of infinite Wordle and infinite Mastermind. The familiar game of Wordle extends naturally to longer words or even infinite words in an idealized language, and Mastermind similarly has natural infinitary analogues. What is the nature of play in these infinite games? Can the codebreaker play so as to win always at a finite stage of play? The analysis emerges gradually, and in the talk I shall begin slowly with some easy elementary observations. By the end, however, we shall engage with sophisticated ideas in descriptive set theory, a kind of infinitary information theory. Some assertions about the minimal size of winning sets of guesses, for example, turn out to be independent of the Zermelo-Fraenkel ZFC axioms of set theory. Some questions remain open.
| 17 - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: TBA
Speaker: Jakub Witaszek – Princeton University 3:00 PM-4:00 PM October 17, 2023 1 Oxford Street, Cambridge, MA 02138 USA Abstract TBA For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar - SEMINARS: Introductory Math Seminar: Contributing Factors to Undergraduate Math Course Decisions
Speaker: Monique Harrison – University of Pennsylvania 3:00 PM-4:00 PM October 17, 2023
Course decision-making is incredibly important for the unfolding of undergraduate pathways, yet consistently understudied. Using data from Harvard’s Math Department and “Western University” another highly selective college, I will highlight some of the mechanisms at play and discuss which factors of students’ backgrounds (gender, class, relationship to math) and university constraints impact these decisions. Building on developing work at Harvard in the fall 2023 semester, I will have some preliminary findings to present and discuss.
| 18 - CMSA EVENT: CMSA New Technologies in Mathematics Seminar: Physics of Language Models: Knowledge Storage, Extraction, and Manipulation
Speaker: Yuanzhi Li – CMU Dept. of Machine Learning 2:00 PM-3:00 PM October 18, 2023 20 Garden Street, Cambridge, MA 02138 Large language models (LLMs) can memorize a massive amount of knowledge during pre-training, but can they effectively use this knowledge at inference time? In this work, we show several striking results about this question. Using a synthetic biography dataset, we first show that even if an LLM achieves zero training loss when pretraining on the biography dataset, it sometimes can not be finetuned to answer questions as simple as “What is the birthday of XXX” at all. We show that sufficient data augmentation during pre-training, such as rewriting the same biography multiple times or simply using the person’s full name in every sentence, can mitigate this issue. Using linear probing, we unravel that such augmentation forces the model to store knowledge about a person in the token embeddings of their name rather than other locations. We then show that LLMs are very bad at manipulating knowledge they learn during pre-training unless a chain of thought is used at inference time. We pretrained an LLM on the synthetic biography dataset, so that it could answer “What is the birthday of XXX” with 100% accuracy. Even so, it could not be further fine-tuned to answer questions like “Is the birthday of XXX even or odd?” directly. Even using Chain of Thought training data only helps the model answer such questions in a CoT manner, not directly. We will also discuss preliminary progress on understanding the scaling law of how large a language model needs to be to store X pieces of knowledge and extract them efficiently. For example, is a 1B parameter language model enough to store all the knowledge of a middle school student? https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09 Password: cmsa - NUMBER THEORY SEMINAR: Number Theory Seminar: Integral points on curves via Baker’s method and finite étale covers
Speaker: Bjorn Poonen – MIT 3:00 PM-4:00 PM October 18, 2023 1 Oxford Street, Cambridge, MA 02138 USA We prove results in the direction of showing that for some affine curves, Baker’s method applied to finite étale covers is insufficient to determine the integral points. - SEMINARS: Informal Seminar on Dynamics, Geometry and Moduli Spaces: Curves in the space of quadratic rational maps
Speaker: E. Hironaka – NSF and FSU 4:00 PM-5:00 PM October 18, 2023 Please see website for more details: www.math.harvard.edu/~ctm/sem. - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Combinatorics of m=1 Grasstopes
Speaker: Yelena Mandelshtram – UC Berkeley 4:15 PM-5:15 PM October 18, 2023
The amplituhedron is an object introduced by physicists in 2013 arising from their study of scattering amplitudes which has garnered much recent attention from physicists and mathematicians alike. Mathematically, it is a linear projection of a nonnegative Grassmannian to a smaller Grassmannian, via a map induced by a totally positive matrix. A Grassmann polytope, or Grasstope, is a generalization of the amplituhedron, defined to be such a projection by any matrix, removing one of the positivity conditions. In this talk, I will discuss joint work with Dmitrii Pavlov and Lizzie Pratt in which we study these objects, with the hope that we may gain new insights by broadening our horizons and studying all Grasstopes. =============================== For more info, see https://math.mit.edu/combin/ - OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood Seminar: How to add things up without “=”
Speaker: Hana Jia Kong – Harvard University 4:30 PM-5:30 PM October 18, 2023 1 Oxford Street, Cambridge, MA 02138 USA
In many mathematical scenarios, the conventional notion of strict equality doesn’t hold. When we work with algebraic operations in such contexts, we need special notions to encode addition, multiplication, and other mathematical operations. In this talk, I will introduce the concept of operads, which serves as an effective tool for this purpose and finds applications across various mathematical fields. =============================== https://people.math.harvard.edu/~gammage/ons/
| 19 - THURSDAY SEMINAR SEMINAR: Thursday Seminar: Topological quantum field theories from finite homotopy types
Speaker: Sanath Devalapurkar – Harvard 3:30 PM-5:30 PM October 19, 2023 1 Oxford Street, Cambridge, MA 02138 USA Thursday Seminar given by Sanath Devalapurkar on “Topological quantum field theories from finite homotopy types.” - SEMINARS: Algebraic Dynamics Seminar: Integer points in orbits on P^1
Speaker: Jit Wu Yap – Harvard 4:00 PM-6:00 PM October 19, 2023 Let f be a rational map on P^1 defined over the rationals Q whose second iterate f^2 is not a polynomial. For x in Q, Silverman has shown that there are only finitely many integers in the forward orbit {x,f(x),…,f^n(x),…}. In this talk, we present results about the more general setting of S-integers in orbits, where S is a finite set of primes, and provide new upper bounds on the number of S-integers in orbits in terms of the size |S|. Please see http://people.math.harvard.edu/~demarco/AlgebraicDynamics/ for more information
| 20 - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Tight Bound and Structural Theorem for Joints
Speaker: Ting-Wei Chao and Hung-Hsun Hans Yu – CMU and Princeton 3:00 PM-4:00 PM October 20, 2023
The joints problem asks to determine the maximum number of joints N lines can form, where a joint in a d-dimensional space is a point on d lines in linearly independent directions. Recently, we determined the maximum exactly for k choose d-1 lines in d-dimensional space, namely k choose d. What is more important is that we are able to prove a structural result determining all optimal configurations, and this is the first success of the polynomial method in this direction. It turns out that our result implies a conjecture of Bollobás and Eccles as an immediate corollary regarding a generalization of the Kruskal–Katona theorem. In this talk, we will talk about the connection to that conjecture and also give a high-level overview of the key ideas. =============================== For more info, see https://math.mit.edu/combin/ - GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR: Gauge Theory and Topology Seminar: Surgery Exact Triangles in Instanton Theory
Speaker: Deeparaj Bhat – MIT 3:30 PM-4:30 PM October 20, 2023 1 Oxford Street, Cambridge, MA 02138 USA
We prove an exact triangle relating the knot instanton homology to the instanton homology of surgeries along the knot. As the knot instanton homology is computable in many instances, this sheds some light on the instanton homology of closed 3-manifolds. We illustrate this with computations in the case of some surgeries on the trefoil which are different from the analogous groups in other Floer theories such as Heegaard Floer and monopole Floer. Finally, we sketch the proof of the triangle.
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22 | 23 - CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: Gauged Linear Sigma Models and Cohomological Field Theories
Speaker: David Favero – University of Minnesota 10:30 AM-11:30 AM October 23, 2023 20 Garden Street, Cambridge, MA 02138 This talk is dedicated to the memory of my friend and collaborator Bumsig Kim and based on joint work with Ciocan-Fontanine–Guere–Kim–Shoemaker. Gauged Linear Sigma Models (GLSMs) serve as a means of interpolating between Kahler geometry and singularity theory. In enumerative geometry, they should specialize to both Gromov-Witten and Fan-Jarvis-Ruan-Witten theory. In joint work with Bumsig Kim (see arXiv:2006.12182), we constructed such enumerative invariants for GLSMs. Furthermore, we proved that these invariants form a Cohomological Field Theory. In this lecture, I will describe GLSMs and Cohomological Field Theories, review the history of their development in enumerative geometry, and discuss the construction of these general invariants. Briefly, the invariants are obtained by forming the analogue of a virtual fundamental class which lives in the twisted Hodge complex over a certain “moduli space of maps to the GLSM”. This virtual fundamental class roughly comes as the Atiyah class of a “virtual matrix factorization” associated to the GLSM data. - CMSA EVENT: CMSA Colloquium: On Provable Copyright Protection for Generative Model
Speaker: Boaz Barak – Harvard University 4:30 PM-5:30 PM October 23, 2023 20 Garden Street, Cambridge, MA 02138 There is a growing concern that learned conditional generative models may output samples that are substantially similar to some copyrighted data C that was in their training set. We give a formal definition of near access-freeness (NAF) and prove bounds on the probability that a model satisfying this definition outputs a sample similar to C, even if C is included in its training set. Roughly speaking, a generative model p is k-NAF if for every potentially copyrighted data C, the output of p diverges by at most k-bits from the output of a model q that did not access C at all. We also give generative model learning algorithms, which efficiently modify the original generative model learning algorithm in a black box manner, that output generative models with strong bounds on the probability of sampling protected content. Furthermore, we provide promising experiments for both language (transformers) and image (diffusion) generative models, showing minimal degradation in output quality while ensuring strong protections against sampling protected content. Joint work with Nikhil Vyas and Sham Kakade. Paper appeared in ICML 2023 and is on https://arxiv.org/abs/2302.10870
| 24 - CMSA EVENT: CMSA General Relativity Seminar: Resolving memory in numerical relativity, and fixing BMS frames for modeling
Speaker: Leo Stein – Mississippi 11:00 AM-12:00 PM October 24, 2023 20 Garden Street, Cambridge, MA 02138
Numerical relativity waveforms serve as ground truth for detection and parameter estimation of binary black hole mergers. Most NR waveforms to date miss memory effects, as they were extracted from simulations using an approximation called extrapolation. I will report on the SXS collaboration’s capacity to resolve memory effects in production NR simulations using Cauchy-characteristic evolution (CCE), and in the future with Cauchy-characteristic matching (CCM). I will further report on how BH perturbation and post-Newtonian theory furnish natural BMS frames. With these BMS frames, we can extract well-defined remnant quantities, perform precision ringdown modeling, and build complete surrogate waveform models that capture memory effects.
Zoom: https://harvard.zoom.us/j/7855806609 Password: cmsa - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: Mirror symmetry and partial compactifications of K3 moduli
Speaker: Mark Gross – Cambridge 3:00 PM-4:00 PM October 24, 2023 1 Oxford Street, Cambridge, MA 02138 USA I will talk about work with Hacking, Keel and Siebert on using mirror constructions to provide partial compactifications of the moduli of K3 surfaces. Starting with a one-parameter maximally unipotent degeneration of Picard rank 19 K3 surfaces, we construct, using methods of myself and Siebert, a mirror family which is defined in a formal neighbourhood of a union of strata of a toric variety whose fan is defined, to first approximation, as the Mori fan of the original degeneration. This formal family may then be glued in to the moduli space of polarized K3 surfaces to obtain a partial compactification. Perhaps the most significant by-product of this construction is the existence of theta functions in this formal neighbourhood, certain canonical bases for sections of powers of the polarizing line bundle. For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar
| 25 - CMSA EVENT: CMSA New Technologies in Mathematics Seminar: Llemma: an open language model for mathematics
Speaker: Sean Welleck – CMU Language Technologies Institute 2:00 PM-3:00 PM October 25, 2023 We present Llemma: 7 billion and 34 billion parameter language models for mathematics. The Llemma models are initialized with Code Llama weights, then trained on the Proof-Pile II, a 55 billion token dataset of mathematical web data, code, and scientific papers. The resulting models show improved mathematical capabilities, and can be adapted to various tasks. For instance, Llemma outperforms the unreleased Minerva model suite on an equi-parameter basis, and is capable of tool use and formal theorem proving without any further fine-tuning. We openly release all artifacts, including the Llemma models, the Proof-Pile II, and code to replicate our experiments. We hope that Llemma serves as a platform for new research and tools at the intersection of generative models and mathematics. https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09 Password: cmsa - NUMBER THEORY SEMINAR: Number Theory Seminar: Towards a unified theory of canonical heights on abelian varieties
Speaker: Padmavathi Srinivasan – ICERM 3:00 PM-4:00 PM October 25, 2023 1 Oxford Street, Cambridge, MA 02138 USA p-adic heights have been a rich source of explicit functions vanishing on rational points on a curve. In this talk, we will outline a new construction of canonical p-adic heights on abelian varieties from p-adic adelic metrics, using p-adic Arakelov theory developed by Besser. This construction closely mirrors Zhang’s construction of canonical real valued heights from real-valued adelic metrics. We will use this new construction to give direct explanations (avoiding p-adic Hodge theory) of the key properties of height pairings needed for the quadratic Chabauty method for rational points. This is joint work with Amnon Besser and Steffen Mueller. - SEMINARS: Informal Seminar on Dynamics, Geometry and Moduli Spaces: Dynamics on blowups of P2
Speaker: Curtis McMullen – Harvard 4:00 PM-5:00 PM October 25, 2023 Please see website for more details: www.math.harvard.edu/~ctm/sem. - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Quasi-random Boolean functions
Speaker: Fan Chung – UCSD 4:15 PM-5:15 PM October 25, 2023
We organize a number of analytic and combinatorial properties of Boolean functions into a hierarchy of equivalence classes in a similar style as quasi-random graphs, but depending on ‘local’ parameters. We construct quasi-random Boolean functions that separate different levels of the quasi-random hierarchy. In addition, we will briefly survey various well known notions of pseudo-randomness for Boolean functions and explore their relations to the quasi-random hierarchy. This is a joint work with N. Sieger. Please note: **special location** MIT 2-449 =============================== For more info, see https://math.mit.edu/combin/
| 26 - CMSA EVENT: CMSA Active Matter Seminar: Scaling behavior and control of nuclear wrinkling
Speaker: Nicolas Romeo – UChicago 1:00 PM-2:00 PM October 26, 2023 20 Garden Street, Cambridge, MA 02138 The cell nucleus is enveloped by a complex membrane, whose wrinkling has been implicated in disease and cellular aging. The biophysical dynamics and spectral evolution of nuclear wrinkling during multicellular development remain poorly understood due to a lack of direct quantitative measurements. We characterize the onset and dynamics of nuclear wrinkling during egg development in the fruit fly when nurse cell nuclei increase in size and display stereotypical wrinkling behaviour. A spectral analysis of three-dimensional high-resolution live-imaging data from several hundred nuclei reveals a robust asymptotic power-law scaling of angular fluctuations consistent with renormalization and scaling predictions from a nonlinear elastic shell model. We further demonstrate that nuclear wrinkling can be reversed through osmotic shock and suppressed by microtubule disruption, providing tunable physical and biological control parameters for probing the mechanical properties of the nuclear envelope, highlighting in passing the importance of nonlinear response to biological robustness.
This seminar will be held in person and on Zoom. https://harvard.zoom.us/j/96657833341 Password: cmsa - THURSDAY SEMINAR SEMINAR: Thursday Seminar: The Ising model as a boundary field theory
Speaker: Cameron Krulewski – MIT 3:30 PM-4:30 PM October 26, 2023 1 Oxford Street, Cambridge, MA 02138 USA Thursday Seminar given by Cameron Krulewski on “The Ising model as a boundary field theory.”
| 27 - CMSA EVENT: Mathematics in Science: Perspectives and Prospects
All day October 27, 2023-October 28, 2023 1 Oxford Street, Cambridge, MA 02138
Mathematics in Science: Perspectives and Prospects A showcase of mathematics in interaction with physics, computer science, biology, and beyond. October 27–28, 2023 Location: Harvard University Science Center Hall D & via Zoom. For more information, please see: https://cmsa.fas.harvard.edu/event/mathematics-in-scien - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Almost all dynamically syndetic sets are multiplicatively thick
Speaker: Daniel Glasscock – UMass Lowell 3:00 PM-4:00 PM October 27, 2023
If a set of integers is syndetic (finitely many translates cover the integers), must it contain two integers whose ratio is a square? No one knows. In the broader context of the disjointness between additive and multiplicative configurations and actions in ergodic Ramsey theory, it makes sense to ask similar questions about dynamically syndetic sets, those sets that contain the visit times of a point to an open set in a minimal topological dynamical system. The main result of the talk is that almost every dynamically syndetic set is multiplicatively very rich: it is “thick” in some coset of a multiplicative subsemigroup. We will discuss some applications: a “thick-starters” van der Waerden theorem; the existence of multiplicative structure in sets of the form A – A + t; and the topological disjointness of minimal niltranslations and minimal, aperiodic multiplicative actions. Time permitting, we will discuss three tools that proved useful in the topic: the prolongation relation (the closure of the orbit-closure relation) developed by Auslander, Akin, and Glasner; the theory of rational points and polynomials on nilmanifolds developed by Leibman, Green, Tao; and the machinery of topological characteristic factors developed recently by Glasner, Huang, Shao, Weiss, and Ye. This talk is based on work in https://arxiv.org/abs/2207.00098. Please note MIT location. =============================== For more info, see https://math.mit.edu/combin/ - GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR: Gauge Theory and Topology Seminar: Quantum UV-IR map and curve counts in skeins
Speaker: Sunghyuk Park – Harvard 3:30 PM-4:30 PM October 27, 2023 1 Oxford Street, Cambridge, MA 02138 USA
Quantum UV-IR map (a.k.a. q-nonabelianization map), introduced by Neitzke and Yan, is a map from UV line defects in a 4d N=2 theory of class S to those of the IR. Mathematically, it can be described as a map between skein modules and is a close cousin of quantum trace map of Bonahon and Wong. In this talk, I will discuss how quantum UV-IR map can be generalized to a map between HOMFLYPT skein modules, using skein-valued curve counts of Ekholm and Shend
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29 | 30 - CMSA EVENT: CMSA Colloquium: Homotopy categories of rings: Some properties and consequences in module categories
Speaker: Manuel Cortés-Izurdiaga – University of Malaga 4:30 PM-5:30 PM October 30, 2023 20 Garden Street, Cambridge, MA 02138 Given a non-necessarily commutative ring with unit and an additive subcategory of the category of right modules, one can consider complexes of modules in the subcategory and the corresponding homotopy category. Sometimes, these homotopy categories are the first step in studying other (algebraic) homotopy categories, such as those associated to a scheme. To study these categories, one can use results from the category of modules or the category of complexes. In the first part of the talk, we will see how some results of homotopy categories of complexes extend to homotopy categories of N-complexes, for a natural number N greater than or equal to 2, using some techniques from module categories, such us the deconstruction of a class of modules. Another approximation is to use other methods for studying homotopy categories, like those coming from triangulated categories. In some cases, the results obtained in homotopy categories imply some consequences in the category of modules. In the second part of the talk, we will see how to prove the existence of Gorenstein-projective precovers for some specific rings using this approach.
| 31 - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: Singularities in mixed characteristic via the Riemann-Hilbert correspondence
Speaker: Jakub Witaszek – Princeton 3:00 PM-4:00 PM October 31, 2023 1 Oxford Street, Cambridge, MA 02138 USA In my talk, I will start by reviewing how various properties of characteristic zero singularities can be understood topologically by ways of the Riemann-Hilbert correspondence. After that, I will explain how similar ideas can be applied in the study of mixed characteristic singularities. This is based on a joint work (in progress) with Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, and Joe Waldron. For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar
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