Purdue Mathematical Physics Seminar
In Fall 2026, the Purdue Mathematical Physics Seminar will be held on Wednesdays 1:00pm - 2:00pm Eastern time in BRNG B206 (when we meet in person) unless otherwise noted. For Zoom meetings, use the link https://purdue-edu.zoom.us/j/96400453765?pwd=OjZzxftaIyhWBIPooh3TxJSUz5ryYH.1 (passcode: 783211)
Fall 2026
September 30 (in-person)
Xuenan Li (Purdue University)
Title: Pseudo-magnetism in a strained discrete honeycomb lattice
Abstract: Slowly-varying nonuniform strain in honeycomb media can generate an effective pseudo-magnetic field, even though the underlying medium is non-magnetic. This phenomenon was first discovered in graphene and later in photonic crystals, and other physical settings. In this talk, I will start from a discrete nearest-neighbor tight-binding model for a nonuniformly strained honeycomb medium. I will then show how this model leads to a continuum magnetic Dirac Hamiltonian that describes wave packets concentrated near a Dirac point of the undeformed structure. I will focus on unidirectional deformations with bounded gradients that preserve translation invariance along the armchair direction. In this setting, we prove the existence of eigenmodes that behave like plane waves along the armchair direction and are strongly localized in the transverse direction, together with quantitative correction estimates. These results apply to deformations that produce an approximately constant pseudo-magnetic field perpendicular to the plane. They also lead to nearly flat bands and, as a consequence, a very high density of states. These analytical results are also supported by numerical simulations of the corresponding deformations. This is joint work with Michael I. Weinstein.
October 21 (Zoom)
Yu Zhao (Tsinghua University)
Title: Supersymmetric Schur functions and the Donaldson-Mochizuki invariants
Abstract: The Weyl integration formula expresses the Hall inner product as a residue, but only in finitely many variables. Using supersymmetric Schur functions, the supercharacters of gl(m|n), I will give a residue formula for the Hall inner product on all symmetric functions. The proof is geometric: it is a Gysin formula for derived Grassmannians of two-term complexes, which also yields a duality for their virtual χ_y-genera. As an application, I will give a new proof of the Nakajima–Yoshioka and Kuhn–Tanaka wall-crossing formula on blow-ups, the key input for blow-up formulas of Donaldson–Mochizuki invariants.
November 4 (in-person)
Dragos Crisan (University of Chicago)
Title: Convolution algebras associated to representations
Abstract: Given a complex reductive group G, a representation V of G and a Borel-stable subspace M of V, we consider the associated Steinberg-type variety Z. We prove that, under a certain condition on (V,M), called gluability, the equivariant Borel-Moore homology or K-theory of Z, equipped with the convolution product, is obtained as the intersection of two copies of the nil-Hecke algebra inside its localization. A similar result holds for quantized Coulomb branches and quantized Iwahori-Coulomb branches. We also provide a description of these algebras in terms of poles and residues, generalizing results of Ginzburg, Kapranov and Vasserot describing the affine Hecke algebra and DAHA, as well as a result of Teleman and Gannon--Webster that realizes certain Coulomb branches by gluing two copies of the universal centralizer.