Calendar
- 05November 5, 2023No events
- 06November 6, 2023
CMSA Algebraic Geometry in String Theory Seminar: Deformations of Landau-Ginzburg models and their fibers
20 Garden Street, Cambridge, MA 02138In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.
CMSA Colloquium: Impossibility results in classical dynamical systems.
20 Garden Street, Cambridge, MA 02138In 1932, motivated by questions in statistical and celestial mechanics, von Neumann proposed classifying the statistical behavior of dynamical systems. In the 1960’s, motivated by work of Poincaré, Smale proposed classifying the qualitative behavior of dynamical systems. These questions laid the groundwork for enormous amounts of work, but the fundamental questions remain open. This talk shows that they are impossible to answer in a rigorous sense. The talk will discuss various kinds of impossibility results and describe how they apply to von Neumann’s program and Smale’s program.
- 07November 7, 2023
CMSA General Relativity Seminar: Fluid stabilization in slowly expanding cosmological spacetimes
20 Garden Street, Cambridge, MA 02138Relativistic fluids are known to form shocks during their evolution from near-homogeneous initial data.
In expanding spacetimes, shock formation is suppressed, if the expansion is sufficiently strong. We refer to this effect as fluid stabilization.
The occurrence of this phenomenon depends on features of the fluid and has implications for our understanding of structure formation and cosmological evolution.
While the effect is well studied in the regime of accelerated expansion, in recent years it has been shown that fluid stabilization occurs as well in spacetimes with slower expansion rates.
In this talk we present different recent results on fluid stabilization in slowly expanding spacetimes and aspects of the methods involved in the respective proofs.Zoom: https://harvard.zoom.us/j/7855806609
Password: cmsa
CANCELLED - Harvard-MIT Algebraic Geometry Seminar: Angle ranks of Abelian varieties
1 Oxford Street, Cambridge, MA 02138 USADue to unforeseen circumstances, his event has been CANCELLED.
I will discuss an elementary notion — the angle rank of a polynomial — and an application to the Tate conjecture for Abelian varieties over finite fields.
For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar
- 08November 8, 2023
CMSA New Technologies in Mathematics Seminar: Peano: Learning Formal Mathematical Reasoning Without Human Data
20 Garden Street, Cambridge, MA 02138Recent progress in game-playing AI has prompted the question: how might we create AIs that master the game of mathematics? Modern interactive theorem provers like Lean or Coq provide most of this analogy by defining states, actions and rewards after given a theorem statement. However, they expose an infinite action space, which makes learning from scratch challenging. I’ll introduce Peano, a minimal theorem-proving environment based on dependent type theory that exposes a finite action space. This feature allows an agent to start tabula rasa in a new domain and learn to solve problems. I’ll first describe a case study on learning to solve simple algebra problems from five sections of the Khan Academy platform. Reinforcement learning alone fails to progress towards the hardest problems, as solutions in terms of the base action space grow longer with increasing problem complexity. Having the agent induce its own tactics — higher-level actions that compress solutions found so far — allows it to make steady progress, solving all problems and guiding it towards human-like solutions. Furthermore, these tactics induce an order to the problems, despite being seen at random during training. The recovered order has significant agreement with the expert-designed Khan Academy curriculum, and second-generation agents trained on the recovered curriculum learn significantly faster. Finally, I’ll describe ongoing work on solving the Natural Number Game — a popular introduction to theorem proving in Lean for mathematicians. The finite action space allows us to train agents by borrowing ideas from curiosity-driven exploration in Reinforcement Learning. Notably, simply trying to find “interesting” consequences of the hypotheses of a theorem — as measured by the surprisal of a language model — often leads to proving the theorem itself.https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09
Password: cmsaNumber Theory Seminar: ℓ-adic images of Galois for elliptic curves over ℚ
1 Oxford Street, Cambridge, MA 02138 USAI will discuss recent joint work with Jeremy Rouse and Drew Sutherland on Mazur’s “Program B” — the classification of the possible “images of Galois” associated to an elliptic curve (equivalently, classification of all rational points on certain modular curves . The main result is a provisional classification of the possible images of -adic Galois representations associated to elliptic curves over ℚ and is provably complete barring the existence of unexpected rational points on modular curves associated to the normalizers of non-split Cartan subgroups and two additional genus 9 modular curves of level 49.
I will also discuss the framework and various applications (for example: a very fast algorithm to rigorously compute the -adic image of Galois of an elliptic curve over ℚ, and then highlight several new ideas from the joint work, including techniques for computing models of modular curves and novel arguments to determine their rational points, a computational approach that works directly with moduli and bypasses defining equations, and (with John Voight) a generalization of Kolyvagin’s theorem to the modular curves we study.
Richard P. Stanley Seminar in Combinatorics: Cross-Ratio Degrees
Given n-3 subsets of {1, …, n} of size 4, the cross-ratio degree counts the number of ways to place n marked points on the Riemann sphere such that the n-3 cross-ratios are prescribed generic complex numbers. If more than k-3 of the sets involve just k of the points, then those k points are overdetermined and the cross-ratio degree vanishes. We show that this is the only reason why a cross-ratio degree can vanish: if no subset of the points is overdetermined, then the cross-ratio degree is positive. This gives a new proof of Laman’s theorem characterizing graphs whose generic embedding in the plane is rigid. Joint with Joshua Brakensiek, Christopher Eur, and Shiyue Li.
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For more info, see https://math.mit.edu/combin/
- 09November 9, 2023
CMSA Active Matter Seminar: Nuclear chromodynamics: non-equilibrium phase transition in the nucleus of a living cell
20 Garden Street, Cambridge, MA 02138Nucleus of a living cell houses a cell genome – a polymer called chromatin, which is a functional form of DNA. It is very long, e.g., 2 meters long for every human cell. Nucleus is also an arena of incessant energy-driven activity. Experiments show that chromatin undergoes large scale motions sustained over long times of order seconds. In the talk, after reviewing the phenomenology, I will show how these flows may arise due to a phase transition in which chromatin-driving motors, such as RNA polymerase, form a polar (“ferromagnetic”) order controlled by hydrodynamic interactions. The talk is based on the joint work with I.Eshghi and A.Zidovska.
Lunch served at 12:30.
This seminar will be held in person and on Zoom.
https://harvard.zoom.us/j/96657833341
Password: cmsa
Thursday Seminar: Invertible field theories and stable homotopy theory
1 Oxford Street, Cambridge, MA 02138 USAThursday Seminar given by Natalia Pacheco-Tallaj on “Invertible field theories and stable homotopy theory.”
- 10November 10, 2023
Gauge Theory and Topology Seminar: Complex Chern-Simons invariants of 3-manifolds via abelianization
1 Oxford Street, Cambridge, MA 02138 USAA hyperbolic 3-manifold M carries a flat PSL(2;C)-connection whose Chern-Simons invariant has been much studied since the early 1980’s. For example, its real part is the volume of M. Explicit formulas in terms of a triangulation involve the dilogarithm. In joint work with Andy Neitzke we use 3-dimensional spectral networks to abelianize the computation of complex Chern-Simons invariants. The locality of the Chern-Simons invariant, expressed in the language of topological field theory, plays an important role. The dilogarithm arises from a novel construction involving Chern-Simons invariants of flat C*-connections over a 2-torus.
- 11November 11, 2023No events