Department of

Mathematics


Seminar Calendar
for events the day of Thursday, February 27, 2020.

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Thursday, February 27, 2020

11:00 am in 241 Altgeld Hall,Thursday, February 27, 2020

The shape of low degree number fields

Bob Hough (Stony Brook University)

Abstract: In his thesis, M. Bhargava proved parameterizations and identified local conditions which he used to give asymptotic counts for $S_4$ quartic and quintic number fields, ordered by discriminant. This talk will discuss results in an ongoing project to add detail to Bhargava's work by considering in addition to the field discriminant, the lattice shape of the ring of integers in the canonical embedding, and by giving strong rates with lower order terms in the asymptotics. These results build on earlier work of Taniguchi-Thorne, Bhargava-Shankar-Tsimerman and Bhargava Harron.

1:00 pm in 464 Loomis ,Thursday, February 27, 2020

Title: Probing heterotic/F-theory duality with a little string theory

Patrick Jefferson (MIT Physics)

Abstract: : The duality between heterotic string theory on a 2-torus and F-theory on an elliptically fibered K3 surface is one of the most groundbreaking results to emerge from the superstring revolution, being intimately related to all other known string dualities. Despite this, a precise map between the moduli spaces of the two theories is only known at special loci. In this talk I will propose a method to compute a general map between moduli spaces. Specifically, I will argue that applying Nekrasovís instanton calculus to a torus-compactified probe little string theory permits an explicit construction of an elliptic fibration in terms of the Narain moduli of the heterotic string. I will also mention potential applications and future prospects for this work.

2:00 pm in 347 Altgeld Hall,Thursday, February 27, 2020

Tracy Widom Distribution and Spherical Spin Glass (Part I)

Qiang Wu (UIUC Math)

Abstract: We studied the global behavior of eigenvalues of random matrices in previous talks. This time we are going to zoom into the bulk to study some local behavior of eigenvalues. In particular, the edge scaling limit of largest eigenvalue is given by the Tracy-widom (TW) distribution, which as a universal object also appears in some other areas, like growth process, spin system and many other interacting particle systems. Taking GUE as our example, we will try to derive the TW distribution represented as a Fredholm determinant with Airy Kernel. Time permits, we will briefly go through the integral representation of TW, and some universality results even extended to the underlying integrable system for general beta ensembles.