• Title: Math Learning Center and Supplemental Instruction in 2017-18
• Date: 03/27/2017
• Time: 4:10 PM - 5:00 PM
• Place: C109 Wells Hall
• Speaker: MLC team and SI team, MSU

We are going to discuss the expected changes to the MLC to be implemented this coming fall. We would also welcome input from faculty and GTAs regarding alternative formats to assist students, including problem/review sessions, etc. The team on Supplemental Instruction will also be join us to acquaint us with plans for SI in Fall '17 and Spring '18. We will discuss possible ways to coordinate these efforts with instructors of large lectures and course coordinators.

• Title: A new physical space approach to improved decay for linear waves with applications
• Date: 03/27/2017
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall
• Speaker: Yannis Angelopoulos, UCLA

I will present a vector field method for the linear wave equation on a wide class of spacetimes through which one can obtain almost optimal energy and pointwise decay results, as well as precise asymptotics. I will also talk about applications of the above method to problems in general relativity. This is joint work with S. Aretakis and D. Gajic.

• Title: What polytopes tell us about toric varieties
• Date: 03/28/2017
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Speaker: Robert Davis, MSU

Polytopes are among the oldest mathematical objects that have been studied. Often, people want to find their volumes, identify triangulations, and describe their lattice points, and more. But why bother doing this? From a combinatorial perspective, the data often answer counting questions that one might have. However, there is much more depth from an algebro-geometric standpoint: this information is often useful for learning about certain toric varieties. In the first of these talks, I will give the background needed to understand what a normal projective toric variety is and how to model them using polytopes. In the second talk, I will define several properties that an algebraic geometer may want to know about a toric variety, and explain how to detect these properties from a purely polytopal perspective.

• Title: Topological Recursion 2
• Date: 03/29/2017
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall
• Speaker: Leonid Chekov, MSU

I will describe the relation between global and local models. Local models are those based on a signle branchpoint. Although a zoo of global models is huge, we have just two types of local models: the Kontsevich model (the Airy kernel) associated with ``dynamic' branchpoints (zeros $\mu_\alpha$ of $dx$ such that $y(\mu_\alpha)\ne \{0,infty\}$) and the Brezin-Gross-Witten model (the Bessel kernel) associated with a 'hard' edge (a zero $a_\alpha$ of $dx$ such that $ydx$ is regular at $a_\alpha$). I will describe the canonical action of quadratic operators establishing exact relations of Ch.-Givental form between a global model and the direct product of local models.

• Title: Hedgehog Bases: A taste of the mathematics and physics of scattering amplitudes
• Date: 03/30/2017
• Time: 11:00 AM - 11:50 AM
• Place: C304 Wells Hall
• Speaker: Daniel Parker, UC Berkeley

Scattering amplitudes are the heart of particle physics, forming a bridge between theory and experiment. The last decade has seen the rise of 'amplitudeology', a program for uncovering the hidden mathematical structures of scattering amplitudes. By importing recent results in mathematics, amplitudeology has produced new insights into scattering amplitudes - such as the 'amplitudehedron' - and translated them into practical computational techniques. In this talk, I will discuss a cluster algebra structure of scattering amplitudes in N=4 Super Yang-Mills theory and deep connections with Goncharov polylogarithms. In order to develop a computational framework which exploits this connection, I show how to construct bases of Goncharov polylogarithms that can be used to describe 6-particle scattering at any order in perturbation theory.

• Title: A Martingale Approach for Fractional Brownian Motions
• Date: 03/30/2017
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall
• Speaker: Jianfeng Zhang, University of Southern California

Empirical studies show that the volatilities could be rough, which typically go beyond the semimartinagle framework and the fractional Brownian Motion (fBM) becomes a natural tool. Compared with BM, fBM has two features: (i) non-Markoivan; (ii) non-semimartingale (when the Hurst parameter $H< {1\over 2}$). We shall show that the recent development of path dependent PDEs provides a convenient tool to extend the standard literature of pricing/hedging derivatives to an fBM framework. This is a joint work with Frederi Viens.

• Title: Harmonic and Dirac-harmonic map
• Date: 03/30/2017
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall
• Speaker: Woong Bae Park, MSU

In this talk we briefly go through harmonic map and Dirac-harmonic map. Especially we see the bubble behavior of harmonic and Dirac-harmonic map and estimates needed.