Wednesday September 13, 2017 1:00 PM  2:00 PM Math Tower P131
 Michael Albanese, Stony Brook University
An Introduction to Geometric Group TheoryAlgebraic topology is a useful tool that allows one to study topology via algebra. For example, we can associate to a space its fundamental group, and studying this group can help us understand the space. In the opposite direction, geometric group theory aims to study groups via an associated space. After explaining how to construct this space, we will discuss how to extract information about the group from it. This will allow us to tackle questions such as: is the fundamental group of a genus two surface isomorphic to a free product of two groups?

Wednesday September 20, 2017 1:00 PM  2:00 PM Math Tower P131
 Jack Burkart, Stony Brook University
Fatou, Julia, and NevanlinnaComplex dynamics concerns itself with the study of the iteration of holomorphic functions. The fundamental objects of study are the Fatou set, where the dynamics are "orderly", and the Julia set, where the dynamics are "chaotic." In this talk, we will define these basic objects and prove similar theorems about them in two different cases: the iteration of rational functions on the Riemann sphere, and the iteration of nonpolynomial entire functions on the plane. Along the way, we will need and introduce some basic concepts in Nevanlinna theory, which studies the value distribution of entire functions, and has applications beyond dynamics in the study of complex differential equations and differential geometry.

Wednesday September 27, 2017 1:00 PM  2:00 PM Math Tower P131
 Yuhan Sun, Stony Brook University
Introduction to Lagrangian embedding problemThrough explicit examples I will introduce why we can and can not embed a Lagrangian of given topological type into C^n. If time permits I will explain how this topic is related with string topology.

Wednesday October 04, 2017 1:00 PM  2:00 PM Math Tower P131
 Matthew Dannenberg, Stony Brook University
An Introduction to P Versus NPStated in one way, the P versus NP problem asks if any computational problem for which a potential solution may be verified in polynomial time must also be solvable in polynomial time. Alternatively, P versus NP is a question about the relative strength of deterministic and nondeterministic computation. In this talk, I will introduce the core ideas of complexity theory through Turing machines. Following this, I will show how P and NP arise naturally through modifications on Turing machine structures. These considerations will lead to the equivalence of the above statements of P versus NP. Further, I will present two oracles such that the oracle classes satisfy P = NP for the first but P != NP for the second.

Wednesday October 11, 2017 1:00 PM  2:00 PM Math Tower P131
 Lisandra Hernandez Vazquez, Stony Brook University
Curvature and TopologyThe main objective of this talk is to provide "geometric intuition" behind the concept of sectional curvature. In the first part of the talk, we'll introduce regular plane curves and an associated notion of curvature, use it to define the Gaussian curvature of a surface and pass from here to sectional curvature of an nmanifold. In the second part, I'll discuss a few topological obstructions to having certain kinds of curvature (positive curvature, negative constant curvature, etc). We'll ultimately address the question as to whether or not curvature determines the inner geometry of a space.

Wednesday October 18, 2017 1:00 PM  2:00 PM Math Tower P131
 John Sheridan, Stony Brook University
The roots of arithmeticWe will recall some wellknown techniques for finding roots of multivariate polynomials over various rings and fields, discuss the hope of a localtoglobal correspondence for finding these roots, and indicate how and why the questions we ask about rootfinding change depending on the situation.

Wednesday October 25, 2017 1:00 PM  2:00 PM Math Tower P131
 YoonJoo Kim, Stony Brook University
Arithmetic and geometry of Dedekind domainsDedekind domain was originally defined in the late 19th century to solve Fermat’s last theorem. Although the attempt was not successful, it turned out Dedekind domains naturally arise in the study of algebraic numbers and Riemann surfaces. This explains a surprising amount of similarities between the two theories. In this talk, we will use the intuition from geometry of Riemann surfaces to understand the analogous results in classical number theory.

Wednesday November 01, 2017 1:00 PM  2:00 PM Math Tower P131
 Chase Middleman, Stony Brook University
TBATBA

Wednesday November 15, 2017 1:00 PM  2:00 PM Math Tower P131
 Tobias Shin, Stony Brook University
TBATBA

Wednesday November 29, 2017 1:00 PM  2:00 PM Math Tower P131
 Jae Ho Cho, Stony Brook University
TBATBA

