Calendar
- 22October 22, 2023No events
- 23October 23, 2023
CMSA Algebraic Geometry in String Theory Seminar: Gauged Linear Sigma Models and Cohomological Field Theories
20 Garden Street, Cambridge, MA 02138This 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 Colloquium: On Provable Copyright Protection for Generative Model
20 Garden Street, Cambridge, MA 02138There 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
- 24October 24, 2023
CMSA General Relativity Seminar: Resolving memory in numerical relativity, and fixing BMS frames for modeling
20 Garden Street, Cambridge, MA 02138Numerical 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: Mirror symmetry and partial compactifications of K3 moduli
1 Oxford Street, Cambridge, MA 02138 USAI 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
- 25October 25, 2023
CMSA New Technologies in Mathematics Seminar: Llemma: an open language model for mathematics
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: cmsaNumber Theory Seminar: Towards a unified theory of canonical heights on abelian varieties
1 Oxford Street, Cambridge, MA 02138 USAp-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.
Informal Seminar on Dynamics, Geometry and Moduli Spaces: Dynamics on blowups of P2
Please see website for more details: www.math.harvard.edu/~ctm/sem.
Richard P. Stanley Seminar in Combinatorics: Quasi-random Boolean functions
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/
- 26October 26, 2023
CMSA Active Matter Seminar: Scaling behavior and control of nuclear wrinkling
20 Garden Street, Cambridge, MA 02138The 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: The Ising model as a boundary field theory
1 Oxford Street, Cambridge, MA 02138 USAThursday Seminar given by Cameron Krulewski on “The Ising model as a boundary field theory.”
- 27October 27, 2023
Mathematics in Science: Perspectives and Prospects
1 Oxford Street, Cambridge, MA 02138Mathematics 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 Richard P. Stanley Seminar in Combinatorics: Almost all dynamically syndetic sets are multiplicatively thick
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 Theory and Topology Seminar: Quantum UV-IR map and curve counts in skeins
1 Oxford Street, Cambridge, MA 02138 USAQuantum 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 - 28October 28, 2023
Mathematics in Science: Perspectives and Prospects
1 Oxford Street, Cambridge, MA 02138Mathematics 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