Calendar
- 30November 30, 2022
Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry
On November 28 – Dec 1, 2022, the CMSA will host a Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry.
For more information, please see: https://cmsa.fas.harvard.edu/event/representation-theory-calabi-yau-manifolds-and-mirror-symmetry/
Number Theory: A p-adic analogue of an algebraization theorem of Borel
1 Oxford Street, Cambridge, MA 02138 USALet S be a Shimura variety such that the connected components of the set of complex points S(C) are of the form D/Γ, where Γ is a torsion-free arithmetic group acting on the Hermitian symmetric domain D. Borel proved that any holomorphic map from any complex algebraic variety into S(C) is an algebraic map. In this talk I shall describe ongoing joint work with Ananth Shankar and Xinwen Zhu, where we prove a p-adic analogue of this result of Borel for compact Shimura varieties of abelian type.
CMSA Probability Seminar: Lipschitz properties of transport maps under a log-Lipschitz condition
Consider the problem of realizing a target probability measure as a push forward, by a transport map, of a given source measure. Typically one thinks about the target measure as being ‘complicated’ while the source is simpler and often more structured. In such a setting, for applications, it is desirable to find Lipschitz transport maps which afford the transfer of analytic properties from the source to the target. The talk will focus on Lipschitz regularity when the target measure satisfies a log-Lipschitz condition.I will present a construction of a transport map, constructed infinitesimally along the Langevin flow, and explain how to analyze its Lipschitz constant. The analysis of this map leads to several new results which apply both to Euclidean spaces and manifolds, and which, at the moment, seem to be out of reach of the classically studied optimal transport theory.Informal Seminar: Triangle groups and Hilbert modular varieties
This seminar will be held in Science Center 530 at 4:00pm on Wednesday, November 30th.
Please see the seminar page for more details: https://www.math.harvard.edu/~ctm/sem
Open Neighborhood: Braid groups, differential equations and quantum groups
1 Oxford Street, Cambridge, MA 02138 USABraids on a given number of strands n can be concatenated and thereby form a group Bn. The latter possesses two different incarnations: it can be presented on a simple set of generators and relations due to E. Artin (1947), or it can be realized as the fundamental group of the space of configurations Xn of n points in the complex plane. I will explain how each of these incarnations leads to a class of representations of Bn. The topological representations arise from differential equations of Xn which are symmetric under the algebra gl_n of nxn matrices. The algebraic representations arise instead from a deformation of this algebra known as the quantum group U_q(gl_n). Finally, I will tie the knot by relating these two classes of representations.