We will begin by discussing some background needed for simplicial groups and simplicial groupoids. We will then show that there is a correspondence between central extensions of simplicial groups A-->... More

Geometric Group Theory is one of the most explored topic in Mathematics for last few decades. In this topic we mostly try to find connections between abstract algebraic properties of groups and geome... More

We will begin by discussing some background needed for simplicial groups and simplicial groupoids. We will then show that there is a correspondence between central extensions of simplicial groups A-->... More

I plan to talk about relatively recent work of E. Katz, J. Rabinoff, and D. Zureick-Brown. These three authors established a uniform bound on the number of rational points in smooth projective algebra... More

2-Stratifolds are a generalization of surfaces where there is a family of disjoint simple closed curves where several sheets meet. They are able to be represented as

bipartite graphs from which... More

A standard result in metric geometry is that every compact geodesic metric space can be approximated arbitrarily well by finite metric graphs in the Gromov-Hausdorff sense. It is well known that the f... More

I will introduce a definition of kissing numbers of a sphere packings in 3-dimensional real space.

We will talk about Greg Kuperberg and Oded Schramn’s Theorem showing that the average number... More

For a monic polynomial in Z[x], the Mahler measure is the product, taken over all roots r, of max{1,|r|}. In some sense, this measures how far a polynomial is from being cyclotomic. We know, from Kro... More

The classification of central extensions of a group $G$ by a

(necessarily abelian) group $A$ is very well understood from both the

Algebra and Geometry viewpoints. Indeed, one of the mos... More

I plan to talk about relatively recent work of E. Katz, J. Rabinoff, and D. Zureick-Brown. These three authors established a uniform bound on the number of rational points in smooth projective algebra... More

We will discuss the idea of the Segre zeta function which in the case of closed subschemes of projective spaces explains how Segre classes behave under the operation of taking cones. Following this, w... More

We begin our study of noncommutative geometry by roughly following the book, Basic Noncommutative Geometry, M. Khalkhali.

Quadratic laminations of the unit disk were introduced by Thurston as a vehicle for understanding the Julia sets of quadratic polynomials and the parameter space of quadratic polynomials. The Central ... More

I plan to talk about relatively recent work of E. Katz, J. Rabinoff, and D. Zureick-Brown. These three authors established a uniform bound on the number of rational points in smooth projective algebra... More

Quadratic laminations of the unit disk were introduced by Thurston as a vehicle for understanding the Julia sets of quadratic polynomials and the parameter space of quadratic polynomials. The Central ... More

We will make the first step towards understanding the recent article on Matrix Weighted Estimates for singular integral operator.





We will begin by presenting the classical sparc... More

We will discuss the idea of the Segre zeta function which in the case of closed subschemes of projective spaces explains how Segre classes behave under the operation of taking cones. Following this, w... More

Roughly speaking a geometric structure is a recipe for gluing together pieces of a geometric space using geometry preserving maps to build a manifold with interesting topology. Some classical examples... More

We prove a formula computing the Chern-Schwartz-MacPherson (CSM) class of an arbitrary subscheme of a nonsingular variety in terms of the Segre class of an associated scheme. This formula generalizes ... More

The octonions are noted for there exceptional symmetry. This can be expressed by examining the size of automorphism group relative to other algebras of a similar size. In particular, the automorphism ... More

We will choose a topic to discuss first.