• Speaker: Arman Tavakoli, MSU
• Title: Introduction to the Yang-Mills equation
• Date: 10/28/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

The Yang-Mills equation is a celebrated topic that is studied in differential geometry and particle physics. We will motivate the equation as a generalization of Maxwell's equations, define the relevant geometrical objects and discuss their properties.

• Speaker: Olga Turanova, MSU
• Title: Partial differential equations from evolutionary ecology
• Date: 10/28/2019
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall

In collaboration with the AWM Student Chapter, we are most happy to welcome Professor Turanova to MSU! The abstract of her talk is: I will describe the analysis of some PDEs that arise as models of ecological and evolutionary processes. There will be (some discussion of) poisonous toads!

• Speaker: Yu Shen, Michigan State
• Title: Serre Duality II
• Date: 10/28/2019
• Time: 4:30 PM - 5:30 PM
• Place: C517 Wells Hall

Serre duality was first proved by Serre in 1950s. It is a very useful tool in algebraic and complex geometry. In this lecture, I will use Čech cohomology to prove Serre duality of projective varieties. If time permits, I would like to talk about some applications of it.

• Speaker: Gorapada Bera, MSU
• Title: Gauge theory and tubular ends
• Date: 10/29/2019
• Time: 12:00 PM - 1:30 PM
• Place: C117 Wells Hall

No abstract available.

• Speaker: Alexander Shapiro, UC Berkeley
• Title: Character varieties, Coulomb branches, and clusters.
• Date: 10/29/2019
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall

Quantum groups admit two different geometric realizations: as quantized character varieties and as quantized Coulomb branches of certain gauge theories. These realizations endow a quantum group with two, a priori different, cluster structures. In this talk I will show these structures, explain why they coincide, and say what they have to do with Gelfand-Tsetlin subalgebras, higher rank Fenchel–Nielsen coordinates, and modular functor from higher Teichmüller theory. This talk will be based on joint works with Gus Schrader.

• Speaker: Aklilu Zeleke, MSU
• Title: New and Old Combinatorial Identities Part II
• Date: 10/30/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

Using a probabilistic approach, we derive some interesting identities involving beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.

• Speaker: Boyu Zhang, Princeton University
• Title: Classification of links with Khovanov homology of minimal rank
• Date: 10/31/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

In this talk, I will present a classification of links whose Khovanov homology has minimal rank, which answers a question asked by Batson and Seed. The proof is based on an excision formula for singular instanton Floer homology that allows the excision surface to intersect the singularity. We will use the excision theorem to define an instanton Floer homology for tangles on sutured manifolds, and show that its gradings detect the generalized Thurston norm for punctured surfaces. This is joint work with Yi Xie.

• Speaker: Robert Pego, Carnegie Mellon University
• Title: Dynamics in models of coagulation and fragmentation
• Date: 10/31/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Coaglation-fragmentation equations are simple, nonlocal models for evolution of the size distribution of clusters, appearing widely in science and technology. But few general analytical results characterize their dynamics. Solutions can exhibit self-similar growth, singular mass transport, and weak or slow approach to equilibrium. I will review some recent results in this vein, discussing: the cutoff phenomenon (as in card shuffling) for Becker-Doering equilibration; stationary and spreading profiles in a data-driven model of fish school size; and temporal oscillations recently found in models lacking detailed balance. A special role is played by Bernstein transforms and complex function theory for Pick or Herglotz functions.

• Speaker: Victor Lie, Purdue University
• Title: A unified approach to three themes in harmonic analysis
• Date: 11/01/2019
• Time: 1:00 PM - 2:00 PM
• Place: C304 Wells Hall

Linked Abstract