Schedule

A Fun Fact About 6

Abstract. It's well known to those who know it well that the symmetric group $S_n$ has trivial outer automorphism group, except for when $n=6$. This expository talk will cover some necessary background before providing a cool proof of the existence of a nontrivial outer automorphism of $S_6$. The construction will use some fun tricks.

Ian Benway, Oklahoma State University

Hermitian rank in ideal powers 

Abstract. We prove that the (hermitian) rank of QP^d is bounded from below by the rank of P^d whenever Q is not identically zero and real-analytic in a neighborhood of some point on the zero set of P in C^n and P is a polynomial of bidegree at most (1,1). This result generalizes the theorem of D'Angelo and Lebl which assumed that P was bihomogeneous. Examples show that no hypothesis can be dropped. This is a joint work with Prof. Jiří Lebl. 

Abdullah Al Helal, Oklahoma State University

Linearization Stability in Conformal Gravity 

Abstract. In this talk, we address the question: When does the first order perturbation theory in Conformal Gravity in dimension 4 work around a given metric?

Siddiqur (Milon) Rahman, Oklahoma State University

Free Resolutions of Monomial Ideals

Abstract. Free resolutions of polynomial ideals I appear as fruitful, albeit complicated, objects in many different areas of mathematics.  The special case where each minimal generator of I is a monomial opens up new tools and perspectives without sacrificing the richness of the topic.  We explain the concept of a free resolution when applied to monomial ideals via an example.  If time permits, we will also touch on the connection between these free resolutions and LCM lattices.  This talk is expository and intended as an introduction to the OSU commutative algebra research interests.

Reid Buchanan, Oklahoma State University

Global Attractors & Reaction-Diffusion Equations. 

Abstract. This talk will begin with a brief discussion on dynamical systems (and PDES, in particular). Then, it will introduce Reaction-Diffusion equations, (RDEs) as well as some relevant definitions needed for the remainder of the discussion. For example, for objects such as (global) attractors, absorbing sets, and Lyapunov functionals. Lastly, one should note that the talk will be rather technical in nature since it will aim to quickly build up the results needed to establish the existence (and subsequent properties) of the global attractor for an RDE. Yet, the specific technicalities will turn out to be widely used (classical and contemporary) results found in analysis, PDEs, and dynamical systems; and thus, these technicalities will be foundational and instructive, especially to those who are interested in such fields. 

Tyler Labus, Oklahoma State University

From Mechanistic to Stochastic Transitions in Metapopulation Modeling of COVID-19 in the United States 

Abstract. : Human mobility is a critical driver of the spatial spread of infectious diseases. In the case of SARS-CoV-2, early outbreaks were largely fueled by the movement of individuals into susceptible populations. To model the initial wave of infections, a hybrid metapopulation framework was introduced [Das et al., 2025, in preparation], capturing both local transmission and inter-regional mobility. As the pandemic evolved, mobility-informed mitigation strategies became increasingly important prior to the widespread availability of vaccines. In this study, we extend the existing framework by incorporating vaccination (V) and death (D) compartments, forming a Susceptible–Vaccinated–Infected–Recovered–Deceased (SVIRD) metapopulation network model. This expanded model enables us to account for disease transmission, immunization efforts, and mortality across spatially connected populations. Applying this framework to COVID-19 data from 77 counties in Oklahoma, we calibrate model parameters to reflect regional transmission dynamics. To better capture the inherent uncertainties in epidemic progression, we further develop a stochastic SVIRD network model. This approach accommodates variability in transmission, recovery, and fatality rates arising from heterogeneity in demographics, immunity, and contact patterns. Our findings highlight the significance of network structure, spatial mobility, and targeted vaccination in shaping outbreak trajectories and guiding effective public health interventions. 

Haridas Das, Oklahoma State University

Nilpotent orbits of complex semi simple lie algebras

Abstract. Nilpotent orbits play a crucial role in representation theory, and they have lots of geometric and combinatorial structures. My plan is to introduce you all to nilpotent orbits of complex semisimple lie algebra, it's classification and its role in representation theory. 

Sachin Chandran, Oklahoma State University