• Title: Update on Quantitative Literacy Courses (MTH 101, 102)
• Date: 03/20/2017
• Time: 4:10 PM - 5:00 PM
• Place: C109 Wells Hall
• Speaker: Bronlyn Wassink, MSU

No abstract available.

• Title: An introduction to Heegaard Floer homology
• Date: 03/20/2017
• Time: 5:30 PM - 6:30 PM
• Place: 
• Speaker: Peter Ozsvath, Princeton

'Knot theory' is the study of closed, embedded curves in three-dimensional space. Classically, knots can be studied via a various computable polynomial invariants, such as the Alexander polynomial. In this first talk, I will recall the basics of knot theory and the Alexander polynomial, and then move on to a more modern knot invariant, 'knot Floer homology', a knot invariant with more algebraic structure associated to a knot. I will describe applications of knot Floer homology to traditional questions in knot theory, and sketch its definition. This knot invariant was originally defined in 2003 in joint work with Zoltan Szabo, and independently by Jake Rasmussen. A combinatorial formulation was given in joint work with Ciprian Manolescu and Sucharit Sarkar in 2006.

• Title: Amplituhedron: Part III
• Date: 03/21/2017
• Time: 2:00 PM - 2:50 PM
• Place: C304 Wells Hall
• Speaker: Eric Bucher, MSU

This talk is the third and final part of our working through the paper by Karp and Williams. We will discuss (finally) the poset structure that you can put on the elements of the m=1 amplituhedron and how they can be made into a hyperplane arrangement.

• Title: Log-Canonical Coordinates for Poisson Brackets
• Date: 03/21/2017
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Speaker: Nicholas Ovenhouse, MSU

In symplectic geometry, Darboux's theorem gives so-called 'canonical' local coordinates, in which the Poisson bracket (obtained from the symplectic structure) takes a particularly simple form: all brackets of coordinate functions are constants. We investigate whether something analogous is true for Poisson varieties (when the coordinate change is only allowed to be rational functions), and give a negative answer in the case of log-canonical coordinates.

• Title: Bordered techniques in Heegaard Floer homology.
• Date: 03/21/2017
• Time: 5:20 PM - 6:20 PM
• Place: 115 International Center
• Speaker: Peter Ozsvath, Princeton

Heegaard Floer homology is a closed three-manifold invariant, defined in joint work with Zoltan Szabo, using methods from symplectic geometry (specifically, the theory of pseudo-holomorphic disks). The inspiration for this invariant comes from gauge theory. In joint work with Robert Lipshitz and Dylan Thurston from 2008, the theory was extended to an invariant for three-manifolds with boundary, 'bordered Floer homology'. I will describe Heegaard Floer homology, motivate its construction, list some of its key properties and applicat

• Title: Topological Recursion
• Date: 03/22/2017
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall
• Speaker: Leonid Chekov, MSU

I begin with solving the loop equations in matrix models. The TR allows constructing in a very algorithmic way all correlation functions $W_s^{(g)}(x_1,\dots,x_s)$ of a model on the base of the spectral curve $\Sigma(x,y)=0$ obtained as a solution of a master loop equation in the planar approximation; the variable $y$ is identified with $W_1^{(0)}$. We are then able to construct all $W_s^{(g)}$ out of this, not very abundant, set of data supplied with the two-point correlation function $W_2^{(0)}(x_1,x_2)dx_1dx_2$, which is a universal Bergmann 2-differential on the spectral curve. We are also able to construct terms of the free energy $F^g$ using the Ch.-Eynard integration formula applied to $W_1^{(g)}$. Finally, I will describe a Feynman-like diagrammatic technique for evaluation all $W_s^{(g)}$.

• Title: Bordered knot invariants
• Date: 03/22/2017
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Speaker: Peter Ozsvath, Princeton

I will describe a bordered construction of knot Floer homology, defined as a computable, combinatorial knot invariant. Generators correspond to Kauffman states, and the differentials have an algebraic interpretation in terms of a certain derived tensor product. I will also explain how methods from bordered Floer homology prove that this invariant indeed computes the holomorphically defined knot Floer homology. This is joint work with Zoltan Szabo.

• Title: The Weil Product
• Date: 03/23/2017
• Time: 11:30 AM - 12:20 PM
• Place: C117 Wells Hall
• Speaker: Charlotte Ure, MSU

No abstract available.

• Title: Phillips Lecture Series
• Date: 03/23/2017
• Time: 2:00 PM - 2:50 PM
• Place: C304 Wells Hall
• Speaker: Peter Ozsvath, Princeton University

No abstract available.

• Title: Conformal split G_2 Holonomy
• Date: 03/23/2017
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall
• Speaker: Ustun Yildirim, MSU

In this talk, we introduce Cartan geometries which are spaces that are locally modeled on homogeneous spaces. We express what conformal geometries are in this language and then move on to study signature (2,3) conformal geometry with holonomy in the split form of G_2 . The exposition will mainly follow https://arxiv.org/abs/1002.1767 chapters 4 and 5.