Calendar
- 19February 19, 2023No events
- 20February 20, 2023No events
- 21February 21, 2023
Harvard–MIT Algebraic Geometry: The period-index problem over the complex numbers
1 Oxford Street, Cambridge, MA 02138 USAThe period-index problem is a longstanding question about the complexity of Brauer classes over a field. I will discuss some Hodge-theoretic aspects of the problem for complex function fields, and give some applications to Brauer groups and the integral Hodge conjecture.
- 22February 22, 2023
CMSA Colloquium: The Black Hole Information Paradox: A Resolution on the Horizon?
20 Garden Street, Cambridge, MA 02138The black hole information paradox — whether information escapes an evaporating black hole or not — remains one of the most longstanding mysteries of theoretical physics. The apparent conflict between validity of semiclassical gravity at low energies and unitarity of quantum mechanics has long been expected to find its resolution in a complete quantum theory of gravity. Recent developments in the holographic dictionary, and in particular its application to entanglement and complexity, however, have shown that a semiclassical analysis of gravitational physics can reproduce a hallmark feature of unitary evolution. I will describe this recent progress and discuss some promising indications of a full resolution of the information paradox.
Number Theory: Hecke algebras for p-adic groups and the explicit local Langlands correspondence for G_2
1 Oxford Street, Cambridge, MA 02138 USAI will talk about my recent joint work with Aubert where we prove the local Langlands conjecture for G_2 (explicitly). This uses our earlier results on Hecke algebras attached to Bernstein components of reductive p-adic groups, as well as an expected property on cuspidal support, along with a list of characterizing properties. In particular, we obtain “mixed” L-packets containing F-singular supercuspidals and non-supercuspidals.CMSA Probability Seminar: Thresholds for edge colorings
We show that if each edge of the complete bipartite graph K_{n,n} is given a random list of C(\log n) colors from [n], then with high probability, there is a proper edge coloring where the color of each edge comes from the corresponding list. We also prove analogous results for Latin squares and Steiner triple systems. This resolves several related conjectures of Johansson, Luria-Simkin, Casselgren-Häggkvist, Simkin, and Kang-Kelly-Kühn-Methuku-
Osthus. I will discuss some of the main ingredients which go into the proof: the Kahn-Kalai conjecture, absorption, and the Lovasz Local Lemma distribution. Based on joint work with Huy Tuan Pham. This seminar will be held on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/probability-seminar/
Informal Seminar: Earthquakes, triangulations and circle homeomorphisms
This seminar will be held in Science Center 530 at 4:00pm on Wednesday, February 22nd.
Please see the seminar page for more details: https://www.math.harvard.edu/~ctm/sem
- 23February 23, 2023
CMSA General Relativity: Quasinormal Modes from Penrose Limits
The purpose of this talk is to give an overview of a semi-global existence result and a trapped surface formation results in the context of the Einstein-Yang-Mills system. Adopting a “signature for decay rates” approach first introduced by An, we develop a novel gauge (and scale) invariant hierarchy of non-linear estimates for the Yang-Mills curvature which, together with the estimates for the gravitational degrees of freedom, yield the desired semi-global existence result. Once semi-global existence has been established, we will explain how the formation of a trapped surface follows from a standard ODE argument. This is joint work with Puskar Mondal and Shing-Tung Yau.
This seminar will be held on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/general-relativity/
Thursday Seminar: Murthy's conjecture
1 Oxford Street, Cambridge, MA 02138 USAThis seminar will take place in SC 507 at 3:30pm.
- 24February 24, 2023
CMSA Algebraic Geometry in String Theory: On the convexity of general inverse $\sigma_k$ equations and some applications
20 Garden Street, Cambridge, MA 02138In this talk, I will show my recent work on general inverse $\sigma_k$ equations and the deformed Hermitian—Yang—Mills equation (hereinafter the dHYM equation). First, I will show my recent results. This result states that if a level set of a general inverse $\sigma_k$ equation (after translation if needed) is contained in the positive orthant, then this level set is convex. As an application, this result justifies the convexity of the Monge—Ampère equation, the J-equation, the dHYM equation, the special Lagrangian equation, etc. Second, I will introduce some semialgebraic sets and a special class of univariate polynomials and give a Positivstellensatz type result. These give a numerical criterion to verify whether the level set will be contained in the positive orthant. Last, as an application, I will prove one of the conjectures by Collins—Jacob—Yau when the dimension equals four. This conjecture states that under the supercritical phase assumption, if there exists a C-subsolution to the dHYM equation, then the dHYM equation is solvable.
This seminar will be held in person and on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event/algebraic-geometry-in-string-theory/
Gauge Theory and Topology: Skein exact triangles in equivariant singular instanton theory
1 Oxford Street, Cambridge, MA 02138 USAGiven a knot or link in the 3-sphere, its Murasugi signature is an integer-valued invariant which can easily be computed from a diagram. Work of Herald and Lin gives an alternative description of knot signatures, as signed counts of SU(2)-representations of the knot group which are traceless around meridians. There is a version of singular instanton homology for links which categorifies the Murasugi signature. We construct unoriented skein exact triangles for these Floer groups, categorifying the behavior of the Murasugi signature under unoriented skein relations. More generally, we construct skein exact triangles in the setting of equivariant singular instanton theory. This is joint work with Ali Daemi.
- 25February 25, 2023No events