Calendar
- 02November 2, 2021
CMSA Algebraic Geometry in String Theory Seminar: Gauss-Manin connection in disguise: Quasi Jacobi forms of index zero
We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomology with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations which are given as vector fields. In the case of elliptic curves we compute explicitly the Gauss-Manin connection and such vector fields. This is a joint work with J. Cao and R. Villaflor. (arXiv:2109.00587)
https://harvard.zoom.us/j/98781914555?pwd=bmVzZGdlRThyUDREMExab20ybmg1Zz09
- 02November 2, 2021
DT-invariants from non-archimedean integrals
Let $M(\beta,\chi)$ be the moduli space of one-dimensional semi-stable sheaves on a del Pezzo surface $S$, supported on an ample curve class $\beta$ and with Euler-characteristic $\chi$. Working over a non-archimedean local field $F$, we define a natural measure on the $F$-points of $M(\beta,\chi)$. We prove that the integral of a certain gerbe on $M(\beta,\chi)$ with respect to this measure is independent of $\chi$ if $S$ is toric. A recent result of Maulik-Shen then implies that these integrals compute the Donaldson-Thomas invariants of $M(\beta,\chi)$. A similar result holds for suitably twisted Higgs bundles. This is joint work with Francesca Carocci and Giulio Orecchia.
- 02November 2, 2021
Quantum algorithms for topological and geometric analysis of data
Quantum computers exhibit a variety of exponential enhancements over classical computers for performing linear algebraic operations. This talk reviews quantum algorithms for algebraic topology: I show how the central problem of simplicial homology can be mapped into a quantum computation, with an exponential speedup over classical algorithms. The method is particularly well adapted to topological analysis of large data sets, including financial time series analysis.
https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09
- 03November 3, 2021
CMSA New Technologies in Mathematics Seminar: When Computer Algebra Meets Satisfiability: A New Approach to Combinatorial Mathematics
Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their excellent search algorithms. This talk will describe a new method for mathematical search that couples SAT solvers with computer algebra systems (CAS), thereby combining the expressiveness of CASs with the search power of SAT solvers. This paradigm has led to a number of results on long-standing mathematical questions such as the first computer-verifiable resolution of Lam’s problem and the discovery of a new infinite class of Williamson matrices.
https://harvard.zoom.us/j/99651364593?pwd=Q1R0RTMrZ2NZQjg1U1ZOaUYzSE02QT09
- 03November 3, 2021
CMSA New Technologies in Mathematics Seminar:When Computer Algebra Meets Satisfiability: A New Approach to Combinatorial Mathematics
Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their excellent search algorithms. This talk will describe a new method for mathematical search that couples SAT solvers with computer algebra systems (CAS), thereby combining the expressiveness of CASs with the search power of SAT solvers. This paradigm has led to a number of results on long-standing mathematical questions such as the first computer-verifiable resolution of Lam’s problem and the discovery of a new infinite class of Williamson matrices.
https://harvard.zoom.us/j/99651364593?pwd=Q1R0RTMrZ2NZQjg1U1ZOaUYzSE02QT09