Colloquium Series | School of Mathematics and Statistical Sciences | SIU

Fall 2024 Speakers

Speaker: Dr. Joseph Hundley
Title: Introduction to Functorial Descent
Date:  10-17-24
Time:  3:00-4:00 pm 
Place: Neckers 156
Abstract: In the theory of automorphic representations, one of the main problems is to construct so-called liftings from representations of smaller matrix groups to those of larger matrix groups. Along with it comes a naturally complementary problem - that of recognizing when a representation of a larger group is a lift, and recovering the representation it was lifted from. Functorial descent is a method, developed by Ginzburg, Rallis and Soudry in the classical groups, of approaching this problem. I will introduce the main ideas with examples from classical groups, and comment on some challenges and new phenomena which emerge in some recent attempts to push the theory into the exceptional groups.

Poster

Speaker: Brendan Martin, Imperial College London
Title: NIRVAR: Network Informed Restricted Vector Autoregression
Date:  10-10-24
Time:  3:00-4:00 pm 
Place: Neckers 156
Abstract: High-dimensional panels of time series arise in many scientific disciplines such as neuroscience, finance, and macroeconomics. Often, co-movements within groups of the panel components occur. Extracting these groupings from the data provides a course-grained description of the complex system in question and can inform subsequent prediction tasks. We develop a novel methodology to model such a panel as a restricted vector autoregressive process, where the coefficient matrix is the weighted adjacency matrix of a stochastic block model. This network time series model, which we call the Network Informed Restricted Vector Autoregression (NIRVAR) model, yields a coefficient matrix that has a sparse block-diagonal structure. We propose an estimation procedure that embeds each panel component in a low-dimensional latent space and clusters the embedded points to recover the blocks of the coefficient matrix. Crucially, the method allows for network-based time series modelling when the underlying network is unobserved. We derive the bias, consistency and asymptotic normality of the NIRVAR estimator. Simulation studies suggest that the NIRVAR estimated embedded points are Gaussian distributed around the ground truth latent positions. On three applications to finance, macroeconomics, and transportation systems, NIRVAR outperforms competing models in terms of prediction and provides interpretable results regarding group recovery.

Poster

Spring 2024 Speakers

Speaker: James T. Gill, Saint Louis University
Title: Distributional Limits, Doubling Metric Spaces, and Lemma
Date:  4-18-24
Time:  3:00-4:00 pm 
Place: Neckers 156
Abstract: In 2001 Benjamini and Schramm proved that the distributional limit of a random graph with bounded degree is almost surely recurrent with respect to the random walk.  To prove this fact they devised an interesting lemma about finite point sets in the plane.  Since then this same lemma has been used several times in different contexts.  In particular, in  joint work with S. Rohde, we used it to show that the uniform infinite planar triangulation is almost surely a parabolic Riemann surface.  In further investigation by the speaker it has been found that the conclusion of this lemma holds in any doubling metric space.  In fact, the metric doubling condition is equivalent to the property described in the lemma.

Poster

Graduate Students "Double-Header" Colloquium
Speaker: Taniya Chandrasena, SIUC
Title: Stochastic SEIR(S) Model with Random Total Population
Date:  4-11-24
Time:  3:00-3:25 pm
Place: Neckers 156
Abstract: The stochastic SEIR(S) model with random total population and random transitions is given by the system of stochastic differential equations:
dS=(-βSI+μ(K-S)+αI+ζR)dt-σ_1 SIF_1 (S,E,I,R)dW_1+σ_4 RF_4 (S,E,I,R)dW_4+σ_5 S(K-N)dW_5
dE=(βSI-(μ+η)E)dt+σ_1 SIF_1 (S,E,I,R)dW_1-σ_2 EF_2 (S,E,I,R)dW_2+σ_5 E(K-N)dW_5
dI=(ηE-(α+γ+μ)I)dt+σ_2 EF_2 (S,E,I,R)dW_2-σ_3 IF_3 (S,E,I,R)dW_3+σ_5 I(K-N)dW_5
dR=(γI-(μ+ζ)R)dt+σ_3 IF_3 (S,E,I,R)dW_3-σ_4 RF_4 (S,E,I,R)dW_4+σ_5 R(K-N)dW_5,
where σ_i>0 and constants α, β, η, γ, ζ, μ≥0. K>0 represents the maximum carrying capacity of total population N. The SDE for the total population N=S+E+I+R has the form
dN(t)=μ(K-N)dt+σ_5 N(K-N)dW_5
on D_0=(0,K). The goal of our study is to prove the existence of unique, Markovian, continuous time solutions on the 5D prism
D={ (S,E,I,R,N)∈R_+^5: 0≤S, E,I,R≤K, N=S+E+I+R≤K }.

Then, using the method of Lyapunov functions, we prove the asymptotic stochastic and moment stability of disease-free and endemic equilibria. Finally, we use numerical simulations to illustrate our results. This is based on the joint work with Prof. Henri Schurz, which was submitted for publication.

Speaker: Dipanjan Mazumdar, School of Physics and Applied Physics, SIUC
Title: Materials-by-design approach
Date:  3-28-24
Time:  3:00-4:00 pm 
Place: Neckers 156
Abstract:  Traditional materials discovery research has relied on what could be described as Edison-like, where several trials are performed to refine a property or by chance. A more recent approach relies on a guided approach where several potential materials are pre-screened theoretically, and only the most promising materials are attempted experimentally. This is often termed a “materials-by-design” approach to accelerate discovery and commercial deployment. This effort is now a federal government initiative under the DMREF program (Designing Materials to Revolutionize and Engineer our Future). In this talk, I will discuss my experience using such an approach. I will share my collaborative work with theorists in identifying new magnetic materials and efforts to realize them experimentally, the challenges of the present approach, and how machine-learning approaches can help overcome these obstacles.

Poster

Speaker: Shanik Chandrasena, SIUC
Title: Stochastic SEIR(S) model with nonrandom total population
Date:  4-4-24
Time:  3:30-3:55 pm 
Place: Neckers 156
Abstract: In this study we are interested on the following 4-dimensional system of stochastic differential equations.  dS=(-βSI+μ(K-S)+αI+ζR)dt-σ_1 SIF_1 (S,E,I,R)dW_1+σ_4 RF_4 (S,E,I,R)dW_4
dE=(βSI-(μ+η)E)dt+σ_1 SIF_1 (S,E,I,R)dW_1-σ_2 EF_2 (S,E,I,R)dW_2
dI=(ηE-(α+γ+μ)I)dt+σ_2 EF_2 (S,E,I,R)dW_2-σ_3 IF_3 (S,E,I,R)dW_3
dR=(γI-(μ+ζ)R)dt+σ_3 IF_3 (S,E,I,R)dW_3-σ_4 RF_4 (S,E,I,R)dW_4 with variance parameters σ_i≥0 and constants α,β,η,γ,μ ζ≥0.
This system may be used to model the dynamics of susceptible, exposed, infected and recovering individuals subject to a present virus with state-dependent random transitions. Our main goal is to prove the existence of a bounded, unique, strong (pathwise), global solution to this system, and to discuss asymptotic stochastic and moment stability of the two equilibrium points, namely the disease free and the endemic equilibria. In this model, as suggested by our advisor, diffusion coefficients can be any local Lipschitz continuous functions on bounded domain D={(S,E,I,R)∈R_+^4:0<S,E,I,R<K,S+E+I+R<K} with fixed constant K>0 of maximum carrying capacity. At the end we carry out some simulations to illustrate our results. This is based on joint work with Prof. Dr. Henri Schurz (SIU), already submitted for publication and currently in revision process.

Poster

Speaker: Rong Fan, Pfizer Inc.
Title: A rank-based approach to improve the efficiency of inferential seamless phase 2/3 clinical trials with dose optimization
Date:  3-21-24
Time:  3:00-4:00 pm 
Place: Neckers 156
Abstract: To accelerate clinical development, seamless 2/3 adaptive design is an attractive strategy to combine phase 2 dose selection with phase 3 confirmatory objectives. As the regulatory requirement for dose optimization in oncology drugs shifted from maximum tolerated dose to maximum effective dose, it’s important to gather more data on multiple candidate doses to inform dose selection. A phase 3 dose may be selected based on phase 2 results and carried forward in phase 3 study. Data obtained from both phases will be combined in the final analysis. In many disease settings biomarker endpoints are utilized for dose selection as they are correlated with the clinical efficacy endpoints. As discussed in Li et al. (2015), the combined analysis may cause type I error inflation due to the correlation and dose selection. Sidak adjustment has been proposed to control the overall type I error by adjusting p-values in phase 2 when performing the combined p-value test. However, this adjustment could be overly conservative as it does not consider the underlying correlations among doses/endpoints. We propose an alternative approach utilizing biomarker rank-based ordered test statistics which takes the rank order of the selected dose and the correlation into consideration. If the correlation is unknown, we propose a rank-based Dunnett adjustment, which includes the traditional Dunnett adjustment as a special case. We show that the proposed method controls the overall type I error, and leads to a uniformly higher power than Sidak adjustment and the traditional Dunnett adjustment under all potential correlation scenarios discussed.

Poster

Speaker: Adrian Clingher, University of Missouri - St. Louis
Title: On Complex Surfaces of Type K3
Date:  2-29-24
Time:  3:00-4:00 pm 
Place: Neckers 156
Abstract:  K3 surfaces are classical objects in complex algebraic geometry, with a rich history dating back to early studies by E. Kummer in 1864. In modern times, research in this area has led to interesting applications in fields as diverse as lattice theory, modular forms, cryptography, and theoretical physics (string theory). In this talk I will present the general properties of K3 surfaces, and also discuss several recent results on a particular class of such objects – K3 surfaces of high Picard rank. 

Speaker's Website

Poster

Speaker: Cheng-Yao Lin, School of Education, SIUC
Title: Ten Different Ways to Answer Why A Negative Times A Negative Is A Positive
Date:  2-22-24
Time:  3:00-4:00 pm 
Place: Neckers 156
Abstract:  Why a negative times another negative is always equal to a positive answer? This is one of the most commonly asked questions in mathematics classes in middle and high school. In this session we will discuss ten different ways to answer why a negative times a negative is a positive. We will use some real–world examples to explain this concept.

Speaker's Website

Poster

Speaker: Jurek "Jerzy" Kocik, SIUC
Title: Metamorphic Life of Circles: Unexpected Connections
Date:  2-15-24
Time:  3:00-4:00 pm 
Place: Neckers 156
Abstract:  In mathematical physics, spinors bring insight into the inner structure of matter. Quite similarly, the spinors of (2+1)-dimensional Minkowski space provide a fresh look at Apollonian disk packings and provide novel results including a parametrization of the integral packings, a fractal visualization of the Apollonian depth function, an alternative derivation of the Descartes' configuration, and more. On the other hand, Apollonian disk packing may be interpreted as a “space-time crystal”. These two seemingly different representations meet strikingly.

Poster