Beginning Of Semester Party &  ...

Jan 23, 2026 Speaker :  Bahareh Baharinezhad

Affiliation:-  Binghamton  University 

Title:-  How to make a million dollars? (Or go broke trying to?) 

Abstract:- My talk focuses on the Nobel Prize–winning work on option pricing by Black and Scholes, with key contributions from Merton. The talk is motivated by a widely shared screenshot of an investor claiming to have turned a $400 investment into one million dollars. Using this example, we will address two central questions:

– How did the market maker on the other side of this trade remain in business?

– To what extent, if at all, can such outcomes be systematically replicated?

Jan 30, 2026 Speaker :  Chloé Postel-Vinay

Affiliation:-  U  Chicago 

Title:-  k-shuffle braid groups

Abstract:- Braid groups are known to arise as from many places, two of which are as the Garside group obtained from the poset of non-crossing partitions, and as the fundamental group of the space of square-free complex polynomials of degree n. The latter is a K(B_n,1) while the former can be used to build a CW-complex with nice combinatorial properties, which is also a K(B_n,1). In 2024, McCammond and Dougherty described explicitly the homotopy allowing to go from one to the other.

In this talk, we introduce a new family of groups called the k-shuffle braid groups. We will see how they arise in two similar contexts: first, we will look at certain families of non-crossing partitions and obtain a (metric) CW-complex following classical arguments from Garside theory for Artin groups. Second, from spaces of complex monic polynomials with a certain set of prescribed regular values. Both spaces also happen to be classifying spaces.

No prior knowledge about braid groups will be assumed.

Website :- sites.google.com/view/cpostelvinay 

Feb. 7, 2026 Speaker :   Miguel Alonso Izquierdo

Affiliation:-   Binghamton University 

Title:- Counting paths. An introduction to Catalan numbers. 

Abstract:-  In this talk I will give an introduction to Catalan numbers, their definition and equivalent constructions, which will naturally lead us to a formula for them and one for a less known sequence,  Ballot numbers. After this, we will use both of these sequences to count the number of elements of different sets.  

Feb. 13, 2026 Speaker :   Miri Son

Affiliation:-  Rice University

Title:-  Classification of SL(n,R)-actions on closed manifolds 

Abstract:-  Recently, Fisher and Melnick classified SL(n,R)-actions on n-dimensional manifolds for n≥3. In this talk, we generalize this result by classifying smooth or real-analytic SL(n,R)-actions on m-dimensional manifolds for 3≤n≤m≤2n-3. This work is motivated by the Zimmer program and is central to it, as Lie group actions restrict to their lattice actions. 

This classification relies on the linearization of SL(n,R)-actions when there is a global fixed point. The analytic case was proved by Guillemin—Sternberg and Kushinirenko. We discuss the smooth case which is ongoing joint work with Insung Park.

Website :- sites.google.com/view/mirison  

Feb. 20, 2026 Speaker :   Junzhi Huang 

Affiliation:-  Yale University 

Title:-  Pseudo-Anosov flows and geometry of transverse surfaces

Abstract:-  Pseudo-Anosov homeomorphisms are a class of interesting homeomorphisms of surfaces. Suspending a pseudo-Anosov homeomorphism in a 3-dimensional pseudo-Anosov mapping tori gives a pseudo-Anosov flow. Such flows turn out to be extremely useful in understanding the topological structure and organizing classes of surfaces in a 3-manifold. I will introduce some basics of pseudo-Anosov homeomorphisms and flows, and then talk about a beautiful result by Cooper-Long-Reid, generalized by Fenley, which shows that the geometry type of a transverse surface can be determined by combinatorial information encoded by the flow.

Website :- sites.google.com/yale.edu/junzhihuang/home 

 Feb 27, 2026 :-  No Seminar  (Rejuvenation Day)