• Speaker: Bartell and Herbel-Eisenmann, MSU
• Title: AIMS: Access, Agency, and Allies in Mathematical Systems
• Date: 02/27/2017
• Time: 12:00 PM - 1:00 PM
• Place: 133G Erickson Hall

In this presentation, we will share information about the AIMS project, on which faculty and doctoral students from eight universities are studying how mathematics teacher educators, mathematics teachers, and students work together to support the fair distribution of opportunities to learn. We will highlight our theoretical focus on access, agency, and allies and the ways in which this has translated into professional development design and will share the story of how two teachers’ adaptations of a PD task supported them in connecting to authentic student experiences and supporting students’ opportunities to learn rigorous mathematics.

• Speaker: Casim Abbas, MSU
• Title: A survey on Legendrian Contact Homology for knots in R^3
• Date: 02/27/2017
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Rachael Lund, Andy Krause, MSU
• Title: RCPD Accommodations
• Date: 02/27/2017
• Time: 4:10 PM - 5:00 PM
• Place: C109 Wells Hall

Rachael, Andy, and Tsveta will be leading a discussion about RCPD accommodations. The goal of the discussion is to gather questions regarding common RCPD accommodations and bring those to the RCPD staff. We hope this will result in developing a guide for instructors and GTAs about how to help students with various RCPD accommodations. For example: • What are some suggestions for providing 50% extended time on a 30-minute quiz if you have another class 20-minutes later? • What are good ways to provide reduced distraction seating for exams? • What are some good ways to work with students who have unexpected absences due to their condition who might miss a quiz or exam that you plan to hand back before they return to school? We invite all of you to share your questions with us so we can bring those to the RCPD to develop a partnership with them to better serve our students.

• Speaker: Chenyun Luo, Johns Hopkins University
• Title: On the motion of a slightly compressible liquid
• Date: 02/27/2017
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

I would like to go over some recent results on the compressible Euler equations with free boundary. We first provide a new a priori energy estimates which are uniform in the sound speed, which leads to the convergence to the solutions of the incompressible Euler equations. This is a joint work with Hans Lindblad. On the other hand, the energy estimates can be generalized to the compressible water wave problem, i.e., the domain that occupied by the fluid is assumed to be unbounded. We are also able to prove weighted energy estimates for a compressible water wave. Our method requires the detailed analysis of the geometry of the moving boundary.

• Speaker: Hugh Thomas, University of Quebec at Montreal
• Title: Describing the amplituhedron
• Date: 02/28/2017
• Time: 2:00 PM - 2:50 PM
• Place: C304 Wells Hall

Amplituhedra were introduced by Arkani-Hamed and Trnka as part of a program to provide an alternative to the classical Feynman diagram approach to scattering amplitudes, via a surprising link with Grassmannian geometry. I will attempt to provide some physics context, and then give the original definition of the amplituhedron (as a certain image of a totally non-negative Grassmannian) and a new proposed definition. This talk is based on joint work with Nima Arkani-Hamed and Jaroslav Trnka.

• Speaker: Emad Zahedi, MSU
• Title: On Distance Preserving and Sequentially Distance Preserving Graphs
• Date: 02/28/2017
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

A graph H is an isometric subgraph of G if d_H(u,v) = d_G(u,v), for every pair u,v in V(H), where d denotes distance. A graph is distance preserving (dp) if it has an isometric subgraph of every possible order. We consider how to add a vertex to a dp graph so that the result is a dp graph. This condition implies that chordal graphs are dp. A graph is sequentially distance preserving (sdp) if its vertices can be ordered such that deleting the first i vertices results in an isometric subgraph, for all i at least 1. We give an equivalent condition to sequentially distance preserving based upon simplicial orderings. Using this condition, we prove that if a graph does not contain any induced cycles of length 5 or greater, then it is sdp. In closing, we discuss our results, other work and open problems concerning dp graphs.

• Speaker: Leonid Chekov, Steklov Institute and MSU
• Title: Topological recursion for matrix models and abstract topological recursion (a course of 3 lectures)
• Date: 03/01/2017
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

I will begin with the description of a generating function for numbers of Grothendieck's dessins d'enfant, or Belyi pairs. This generating function is given by a random matrix model integral, I describe what is a topological expansion (AKA genus expansion) of such models. The method allowing finding corrections in all orders of the genus expansion is Topological Recursion formulated in its present form by Eynard, Orantin and the speaker in 2005-2006. This method had already found numerous applications in mathematics and mathematical physics, so I describe the general construction underlying the topological recursion and present an (incomplete) list of its applications. Very recently, this method was developed into an abstract topological recursion by Kontsevich and Soibelman. In my last lecture I explain their construction and our interpretation of it (forthcoming paper by J.Andersen, G.Borot, L.Ch., and N.Orantin).

• Speaker: Thomas Plante, MSU
• Title: Elliptic Curves over Finite Fields
• Date: 03/02/2017
• Time: 11:30 AM - 12:20 PM
• Place: C117 Wells Hall

No abstract available.

• Speaker: Corey Bregman, Rice University
• Title: The genus of a special cube complex and its applications
• Date: 03/02/2017
• Time: 2:00 PM - 2:50 PM
• Place: C304 Wells Hall

Recently, the geometry of non-positively curved (NPC) cube complexes has featured prominently in low-dimensional topology. We introduce an invariant of NPC special cube complexes called the genus, which generalizes the classical notion of genus for a closed orientable surface. We then show that having genus one characterizes special cube complexes with abelian fundamental group and discuss some applications.

• Speaker: Wenzhao Chen, MSU
• Title: Genus two mutant knots
• Date: 03/02/2017
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

In this talk, I will give an introduction to the so called mutation operation of a 3-manifold, which can be described as cutting the 3-manifold along a given surface and then sew it back in a different way. In particular, this induces corresponding mutation operations on knots obtained by mutating the 3-sphere along a genus 2 surface in the knot complement. I will survey a few properties and conjectures regarding mutant knots.

• Speaker: Qing Han, University of Notre Dame
• Title: Singular solutions of the Yamabe equation
• Date: 03/03/2017
• Time: 4:10 AM - 5:00 AM
• Place: C304 Wells Hall

In a classical paper, Cafferelli, Gidas and Spruck discussed positive solutions of the Yamabe equation, corresponding to the positive scalar curvature of the conformal metrics, with a nonremovable isolated singularity. They proved that solutions are asymptotic to radial singular solutions. Korevaar, Mazzeo, Pacard, and Schoen expanded solutions to the next order. In this talk, we discuss how to expand solutions up to arbitrary order. We also discuss positive solutions of the Yamabe equation, corresponding to the negative scalar curvature of the conformal metrics, that become singular in an (n-1)-dimensional set.