Colloquia & Seminars

Title: A combinatorial formula for interpolation Macdonald polynomials

Member Seminar Speaker: Houcine Ben Dali, Harvard CMSA Title: A combinatorial formula for interpolation Macdonald polynomials Abstract: In 1996, Knop and Sahi introduced a remarkable family of inhomogeneous symmetric polynomials, defined via vanishing conditions, whose top homogeneous parts are exactly the Macdonald polynomials. Like the Macdonald polynomials, these interpolation Macdonald polynomials are closely connected to the Hecke algebra, and admit nonsymmetric versions, which generalize the nonsymmetric Macdonald polynomials. I will present a combinatorial formula for interpolation Macdonald polynomials in terms of signed multiline queues. This formula generalizes the combinatorial formula for Macdonald polynomials in terms of multiline queues given by Corteel–Mandelshtam–Williams. This is based on a joint work with Lauren Williams.

Title: Computing WKB periods 

Quantum Field Theory and Physical Mathematics Seminar Speaker: Max Meynig, University of Connecticut Title: Computing WKB periods Abstract:  In one dimensional quantum mechanics, the all-orders WKB method leads to ‘quantum periods’ which are formal power series in \hbar whose coefficients are certain period integrals. These periods, which limelight in supersymmetric/string theories, have rich structure and can be computed in a number of ways. I will discuss a new perspective on them and their computation.

Title: Recent Advances in Probabilistically Checkable Proofs

Colloquium Speaker: Dor Minzer (MIT) Title: Recent Advances in Probabilistically Checkable Proofs Abstract: The PCP Theorem is a cornerstone of computer science, with applications to hardness of approximation, verification, interactive protocols and more. It asserts a witness for the satisfiability of a given 3CNF formula can be encoded in a robust way that allows local checking.In this talk we discuss recent developments in PCPs, and their connection with distributed protocols, high-dimensional expanders and discrete Fourier analysis. Based on joint works with Kai Zhe Zheng, Mitali Bafna, Noam Lifshitz, Nikhil Vyas.

Title: Aganagic’s invariant is Khovanov homology

Geometry and Quantum Theory Seminar Speaker: Lorenzo Riva, CMSA Title: Aganagic’s invariant is Khovanov homology    

Title: Covers of curves, Ceresa cycles, and unlikely intersections

Algebra Seminar Speaker: Padamavathi Srinivasan, Boston University Title: Covers of curves, Ceresa cycles, and unlikely intersections Abstract: The Ceresa cycle is a canonical homologically trivial algebraic cycle associated to a curve in its Jacobian. In his 1983 thesis, Ceresa showed that this cycle is algebraically nontrivial for a very general complex curve of genus at least 3. In the last few years, there have been many new results shedding light on the locus in the moduli space of genus g curves where the Ceresa cycle becomes torsion. We will survey these recent results and provide new examples of positive dimensional families of curves where only finitely many members of the family have torsion Ceresa cycle. The main idea is...

Title: Member Seminar

Member Seminar Speaker: tba

Title: The active Young-Dupré Equation

Colloquium Speaker: Julien Tailleur, MIT Title: The active Young-Dupré Equation Abstract: The Young-Dupré equation is a cornerstone of the equilibrium theory of capillary and wetting phenomena. In the biological world, interfacial phenomena are ubiquitous, from the spreading of bacterial colonies to tissue growth and flocking of birds, but the description of such active systems escapes the realm of equilibrium physics. I will show how a microscopic, mechanical definition of surface tension allows building an Active Young-Dupré equation able to account for the partial wetting observed in simulations of active particles interacting via pairwise forces. Remarkably, the equation shows that the corresponding steady interfaces do not result from a simple balance between the surface tensions at play but instead...

Title: Geometry and Quantum Theory Seminar

Geometry and Quantum Theory Seminar Speaker: tba

Title: Member Seminar

Member Seminar Speaker: tba