• Speaker: Meihua Tu, Medicine Design, Pfizer Inc.
• Title: The role of water molecules in Ketohexokinase (KHK) inhibitor design
• Date: 12/02/2019
• Time: 10:00 AM - 11:00 AM
• Place: C304 Wells Hall

Increased fructose consumption and its subsequent metabolism have been implicated in hepatic steatosis, dyslipidemia, obesity, and insulin resistance in humans. Since ketohexokinase (KHK) is the principal enzyme responsible for fructose metabolism, inhibition of KHK may ameliorate non-​alcoholic fatty liver disease (NAFLD) and non-​alcoholic steatohepatitis (NASH) by decreasing fructose conversion to fructose-​1-​phosphate. Initial low MW hits were identified by fragment screening. A combination of parallel synthesis and structure-​based drug design yielded a clinic candidate, currently in clinic trials. This presentation will focus on computational techniques that have been applied in the optimization of lead compounds. In particular, how water molecule energy profile in the binding pocket was used to guide compound design. Our successful fragment-​to-​candidate story will demonstrate the power of combining structure-​based drug design with parallel chem.

• Speaker: Sanjay Kumar, MSU
• Title: An Introduction to Link Invariants from Tangle Operators
• Date: 12/02/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

In the early 90’s, Reshetikhin and Turaev constructed topological invariants of 3-manifoolds and of framed links in 3-manifolds using quantum groups. In this talk, I will introduce their approach with specific examples and show how they relate to known link invariants such as the Jones polynomial.

• Speaker: Matt Hedden, MSU
• Title: Spectral sequences in Floer theory (ctd)
• Date: 12/03/2019
• Time: 12:00 PM - 1:30 PM
• Place: C117 Wells Hall

Talk continued from 2 weeks prior

• Speaker: Shelly Harvey, Rice
• Title: Pure braids and link concordance
• Date: 12/05/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

If one considers the set of m-component based links in R^3 with a 4-dimensional equivalence relationship on it, called concordance, one can form a group called the link concordance group, C^m. Questions in concordance are important in for classification questions in topological and smooth 4-manifolds It is well known that the link concordance group contains the isotopy class of pure braid with m strands, P_m. That is, two braids are concordant if and only if they are isotopic! In the late 90's Tim Cochran, Kent Orr, and Peter Teichner defined a filtration of the knot/link concordance group called the n-solvable filtration. This filtration gives a way to approximate whether a link is trivial in the group. We discuss the relationship between pure braids and the n-solvable filtration as well as various other more geometrically defined filtrations coming from gropes and Whitney towers. This is joint work with Aru Ray and Jung Hwan Park.

• Speaker: Luca Di Cerbo, University of Florida
• Title: Price Inequalities and Benjamini-Schramm Convergence
• Date: 12/10/2019
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall

In this talk, I will present a study of Betti numbers of sequences of compact negatively curved Riemannian manifolds Benjamini-Schramm converging to their universal covers. The main tools are a Price inequality for harmonic forms on negatively curved spaces, and an effective thick-thin decomposition.

• Speaker: Matthew Stoffregen, Massachusetts Institute of Technology
• Title: Smooth 4-manifolds and the geometry of 3-manifolds
• Date: 12/10/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

One of the interests of low-dimensional topologists is understanding which smooth 4-manifolds can bound a given 3-manifold, or, as a special case, understanding the set of 3-manifolds up to so-called homology cobordism (to be defined in the talk). This question turns out to have applications to the study of triangulations of high-dimensional manifolds, and is a natural proving ground for Floer-theoretic techniques of studying 3-manifolds. In this talk, we will give some structure theorems about the homology cobordism group, and show that there are three-manifolds that are very far from having any of the seven non-hyperbolic Thurston geometries. This talk includes joint work with I. Dai, K. Hendricks, J. Hom, L. Truong, and I. Zemke.

• Speaker: Antonio De Rosa, New York University
• Title:  Elliptic integrands in geometric variational problems
• Date: 12/11/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Elliptic integrands are used to model anisotropic energies in variational problems. These energies are employed in a variety of applications, such as crystal structures, capillarity problems and gravitational fields, to account for preferred inhomogeneous and directionally dependent configurations. After a brief introduction to variational problems involving elliptic integrands, I will present an overview of the techniques I have developed to prove existence, regularity and uniqueness properties of the critical points of anisotropic energies. In particular, I will present the anisotropic extension of Allard's rectifiability theorem and its applications to the Plateau problem. Furthermore, I will describe the anisotropic counterpart of Alexandrov's characterization of volume-constrained critical points. Finally, I will mention some of my ongoing and future research projects.

• Speaker: Zhouli Xu, Massachusetts Institute of Technology
• Title: In and around stable homotopy groups of spheres
• Date: 12/12/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

The computation of stable homotopy groups of spheres is one of the most fundamental problems in topology. Despite its simple definition, it is notoriously hard to compute. It has connections to many areas of mathematics. In this talk, I will discuss a recent breakthrough on this problem, which depends on motivic homotopy theory in a critical way. I will also talk about applications to smooth structures on spheres, and towards the open problem of Kervaire invariant one in dimension 126. This talk is based on several joint work with Bogdan Gheorghe, Daniel Isaksen, and Guozhen Wang.