Boston Graduate Math Colloquium

This is a joint collaboration between graduate students and PhD candidates in Boston who happen to know each other. The aim is to provide a venue for grad students at all levels to give math talks accessible to a general audience, and meet fellow researchers who are right down the street or across the river. BU, Northeastern, BC, and Harvard will host four events throughout the academic year. Each Saturday will consist of 4-5 speakers discussing their research.

Date & Location

Date: Sat. 10/13

Location: Room 148 in MCS. 111 Cummington Mall, Boston, MA 02215.

RSVP

Please use this so we can order enough food!

Schedule

10-10:30: Coffee and Breakfast

10:30-11: Jim LaDeuce (BU) - A Quick Introduction to Gauge Theory

11-12 : Mikhail Mironov (NEU) - Exceptional objects and exceptional collections in derived categories

12-1 : Lunch

1-2 : Eric Cooper (BU) - Selection of quasi-stationary states in 2d Stochastic Navier-Stokes on the symmetric and asymmetric torus

2-2:30: Anthea Chung (BU) - Spatio-temporal patterns in the wake of pulse solutions to the Morris-Lecar neuron model

2:30-3: Afternoon Coffee/Tea

3-4: Clayton McDonald (BC) - Slicing 2-knots

Speakers, Titles, and Abstracts

Jim LaDeuce, Boston University

A Quick Introduction to Gauge Theory

Abstract: In physics, the mathematical description of a system often contains excess degrees of freedom. The transformations between the descriptions that correspond to the same physical configuration form a group called the gauge group. In many examples, the space of physically realizable systems will be described by the space of connections on some principal G-bundle modulo the gauge group. In this talk, I will attempt to identify and explain the various mathematical components of a gauge theory from the perspective of perturbative field theory. Time permitting, I will also discuss how quantization enters the picture.

Mikhail Mironov, Northeastern University

Exceptional objects and exceptional collections in derived categories

Abstract: The bounded derived category of coherent sheaves is the main homological invariant of an algebraic variety, capturing the most essential geometric information. It stands in the focus of many recent research papers. One of the ways to describe it is via an exceptional collection.

In my talk I will define derived categories, exceptional collections and Lefschetz collections and try to convince you that these are reasonable things to consider. I am particularly interested in S_k-invariant exceptional collections on products of k projective spaces. I will give examples of known exceptional collections and present the results of my research in that area.

Eric Cooper, Boston University

Selection of quasi-stationary states in 2d Stochastic Navier-Stokes on the symmetric and asymmetric torus

Abstract: Recent numerical studies have revealed certain families of functions play a crucial role in the long time behavior of 2D Navier-Stokes with periodic boundary conditions. These functions, called bar and dipole states, exist as quasi-stationary solutions and attract trajectories of all other initial conditions exponentially fast. If the domain is the symmetric torus, then the dipole states dominate, while on the asymmetric torus the bar states dominate. Using the vorticity equation, we will formulate a mathematical framework to explain the evolution of solutions toward these metastable states in both a deterministic and stochastic setting.

Anthea Chung, Boston University

Spatio-temporal patterns in the wake of pulse solutions to the Morris-Lecar neuron model

Abstract: TBD

Clayton McDonald, Boston College

Slicing 2-knots

Abstract: I will talk about a process for creating interesting slices of knotted surfaces, and talk about associated knot invariants and embedding problems of 3 manifolds into 4 manifolds.


Past Colloquiua

Boston University, Oct 21 2017. Speakers: Brian Hepler, Spencer Leslie, Jackson Walters, Yusheng Luo.

Northeastern University, Dec 2 2017. Speakers: Angus McAndrew, Eric Chang, Maria Fox, Emre Sen.

Boston College, Feb 10 2018. Speakers: Brian Choi, Roderic Guigo, Rahul Singh, Ben Thompson, Shucheng Yu

Harvard University, Apr 28 2018. Speakers: Siddhi Krishna, Jessica Nadalin, Monika Pickler, Elizabeth Upton, Ying Zhang