Colloquium Series

+++Archives+++

[4-18-2024] James T. Gill, Saint Louis University

Title: Distributional Limits, Doubling Metric Spaces, and Lemma

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.

[4-11-2024]  Graduate Students "Double-Header" Colloquium II

Speaker: Taniya Chandrasena, SIUC
Title: Stochastic SEIR(S) Model with Random Total Population
Time:  3:00-3:25 pm
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: Mohammed Mousa A M Alshamrani, SIUC

Title: Simple Smale Flows with a Three-Band Template

Time:  3:30-3:55 pm 

Abstract: A Smale flow is a structurally stable flow with one-dimensional invariant sets. We study Smale flow with chain recurrent sets consisting of an attracting closed orbit, a repelling closed orbit, and a saddle set that is a suspension of a full 3-shift. We use tools from template theory to construct and visualize nonsingular Smale flows in the 3-sphere.

[4-4-2024]  Graduate Students "Double-Header" Colloquium I

Speaker: Devjani Basu, SIUC
Title: Modular Representations of the Special Linear Groups over a Finite Field
Time:  3:00-3:25 pm
Abstract:  Let p be a prime number, Fq a finite field of q elements, where q is a power of p and F be its algebraic closure. The modular representations of the group SLn(Fq) are the representations over the field with characteristic l > 0. Our study is restricted to the case of equal characteristic, i.e. l = p. The overarching goal is to describe all the irreducible modular representations of SLn(Fq), explicitly, as vector spaces. Owing to the nature of SLn(Fq) as a finite group of Lie Type, we employ time-honored methods as well as explore new techniques to accomplish our goal.

Speaker: Shanik Chandrasena, SIUC
Title: Stochastic SEIR(S) model with nonrandom total population
Time:  3:30-3:55 pm
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.

[3-28-2024] Dipanjan Mazumdar, School of Physics and Applied Physics, SIUC

Title: Materials-by-design approach

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.

[3-21-2024] Rong Fan, Pfizer Inc.

Title: Metamorphic Life of Circles: Unexpected Connections

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.

[2-29-2024] Adrian Clingher, University of Missouri - St. Louis

Title: On Complex Surfaces of Type K3

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. 

[2-22-2024]  Cheng-Yao Lin, School of Education, SIUC

Title: Ten Different Ways to Answer Why A Negative Times A Negative Is A Positive

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.

[2-15-2024]  Jerzy Kocik, SIUC

Title: Metamorphic Life of Circles: Unexpected Connections

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.

[11-16-2023]  Alejandra Alvarado, Eastern Illinois University

Title: Arithmetic Progressions on Curves

Abstract:  The study of arithmetic progressions has been around for centuries. But the study of arithmetic progressions on curves is more recent. In particular, what is the longest arithmetic progression on elliptic curves? We give a survey of some results.

[10-26-2023]  Karol Koziol, Baruch College, CUNY

Title: An introduction to the mod p Langlands Program

Abstract:  One of the crowning achievements of 20th century mathematics is Class Field Theory, which has its origins in Gauss' Law of Quadratic Reciprocity, and which (among other things) gives a description of all abelian field extensions of the rational numbers.  This turns out to be the beginning of the Langlands Program, a wide-ranging web of conjectures that connects the areas of Number Theory, Representation Theory, and Algebraic Geometry.  I'll give an introduction to this circle of ideas, and discuss a fairly recent development: the mod p, "local" version of these conjectures.  I'll also indicate how this variant can be used to shed light on some questions arising from geometry.

[10-5-2023]  Ali Mehrabani, School of Analytics, Finance and Economics, SIUC

Title: Estimation and Identification of Latent Group Structures in Panel Data with Interactive Fixed Effects

Abstract: This paper provides a framework for joint estimation and identification of latent group structures in panel data models with interactive fixed effects using a pairwise fusion penalized approach. The latent structure of the model allows individuals to be classified into different groups where the number of groups and the group membership are unknown. A penalized principal component (PPC) estimation procedure is introduced to detect the latent group structure. To implement the proposed approach, an alternating direction method of multipliers algorithm has been developed. The proposed method is further illustrated by simulation studies and an empirical application of economic growth which demonstrate the performance of the method. 

[9-28-2023] Mohamad Kazem Shirani Faradonbeh, Southern Methodist University

Title:  Learning from Multiple Multivariate Time-Series

Abstract: Autoregressive models are among the most popular ones for analyzing temporally dependent data. However, little is known about learning from multiple time-series trajectories, especially when it comes to multi-dimensional and non-stationary data. We study this problem and propose a joint estimation method for learning transition matrices of multiple vector autoregressive models that are unknown linear combinations of some unknown basis matrices. The setting is technically challenging due to high dimensionality of the parameter space as well as the compound nature of the uncertainty. Still, our theoretical analysis shows that the proposed joint estimator has an optimal sample-complexity and excels individual learning methods. Furthermore, applications to data-driven stabilization of dynamical systems through exogenously designed input experiments will be discussed. 

[9-7-2023] Jun Liu, SIUE

Title: Direct Parallel-in-Time Solvers and Backward Heat Conduction Problem

Abstract:  In this talk, I will first briefly introduce some parallel in time (PinT) algorithms, including the widely used parareal algorithm and the diagonalization-based algorithms. I will then present our new well-conditioned direct PinT solvers, which show promising parallel efficiency for solving time-dependent differential equations (ODEs and PDEs). As an application, I will show how PinT algorithms can be applied to inverse PDE problems. Within the framework of quasi-boundary value method (QBVM), we designed a direct PinT solver for the ill-posed Backward Heat Conduction Problem. The novel idea is to maneuver the flexibility of regularization for better structured systems that enable fast diagonalization. The high efficiency of the proposed PinT algorithms is illustrated by numerical examples.

[4-27-2023] Ravindra Girivaru, University of Missouri-St. Louis

Title: Matrix factorizations of polynomials

Abstract: A matrix factorization of a polynomial F is a pair of (square) matrices (A, B) such that their product is F times the identity matrix. After spending some time on preliminaries, I will explain what is known about this question, and what its relevance is to the geometry of the set of zeroes of the polynomial F.  I will also talk about its connection to the problem of determining the minimum number of polynomials required to define curves in  three dimensional space and analogous questions. This talk should be accessible to undergraduates in the department.

[4-6-2023] Natasha Dobrinen, University of Notre Dame

Title: Ramsey theory on binary relational homogeneous structures

Abstract: Generalizations of Ramsey's Theorem to colorings of infinite sets proceed via topological considerations.  The Galvin-Prikry Theorem states that Borel subsets of the Baire space are Ramsey.  Silver extended this to analytic sets, and Ellentuck gave a topological characterization of Ramsey sets in terms of the property of Baire in the Vietoris topology. 

We present work extending these theorems to several classes of countable homogeneous structures, answering a question of Kechris, Pestov, and Todorcevic.  An obstruction to exact analogues of Galvin-Prikry or Ellentuck is the presence of big Ramsey degrees.  We will discuss how different properties of the structures affect which analogues have been proved.  Presented is work of the speaker for SDAP+ structures, and joint work with Zucker for binary finitely constrained FAP classes.  A feature of the work with Zucker is showing that we can weaken one of Todorcevic's four axioms guaranteeing a Ramsey space, and still achieve the same conclusion.  These axioms are built on prior work of Carlson and Simpson developing topological Ramsey space theory.

[3-2-2023] Yu Jin, SIUC

Title: Actuary Profession: A Career in Analyzing Risks and Managing Uncertainty 

Abstract: Actuaries are professionals who use mathematical models to analyze and quantify financial risks, particularly in the areas of insurance, pension plans, and investments. With the growing complexity of modern business, the demand for actuaries is steadily increasing, as they help organizations manage and mitigate financial risks, and make strategic decisions based on data-driven insights.

This presentation will provide an overview of the actuary profession, including the key skills required, the education and certification requirements, and the typical career path for aspiring actuaries. We will explore the various fields in which actuaries work, such as life and health insurance, property and casualty insurance, consulting, and government. We will also discuss the challenges and opportunities facing the actuarial profession in today's rapidly changing business environment, and the importance of staying current with emerging trends and technologies.

The presentation will conclude with a discussion of the rewards and benefits of pursuing a career as an actuary, including job security, high earning potential, and the opportunity to make a meaningful impact on society. Whether you are a student exploring career options or a professional looking to transition into a new field, this presentation will provide valuable insights into the actuary profession and its role in managing risks and uncertainties in today's economy. 

[2-9-23] Bhaskar Bhattacharya, SIUC 

Title: Effect of misspecification of dependence in constrained statistical inference 

Abstract: The assumption of independent observations that underlies many statistical procedures is called into question when analyzing complex survey data. In clustered data, for example, two-stage samples exhibit positive intra-cluster correlation. Wu, et. al. (1988) showed that ignoring such correlations leads to serious consequences such as much larger variances of the estimates of regression coefficients and inflated type I error rates of the corresponding F-statistic. Misspecification of dependence in observations can happen in a more general setup beyond clustered data. We investigate how to adjust the conventional statistical inference in presence of inequalities when dependent samples are taken from the normal distribution. We extend the study to hypotheses testing in a constrained regression model. We analyze Covid data from 2020 to investigate the presence of trend using the procedure developed.  

[2-9-23] Lindsey-Kay Lauderdale, SIUC 

Title: On a new invariant: the action-genus of a finite group

Abstract: In this talk, we will define a new invariant for finite groups, called the action-genus. Let G be a finite group. Among all graphs Γ whose automorphism group is isomorphic to G, define the action-genus of G to be the minimal genus of a closed connected orientable surface on which Γ can be cellularly embedded. Here, we will elucidate some basic properties for the action-genus of a finite group, establish the action-genus of a few infinite families of finite groups, and then conclude with some open questions about the action-genus of finite groups in general.

[11-10-22]  Steven Senger, Missouri State University

Title: Using graph theory, additive number theory, and geometric measure theory to study finite point configurations

Abstract: In 1946 Paul Erdős asked for asymptotic estimates on how often a single distance could occur in a large finite point set in the plane. We discuss this and related problems, touching on methods from graph theory, additive number theory, and geometric measure theory. We will also look at a variety of settings, from discrete point sets and fractals in Euclidean space, to vector spaces over finite fields, and other algebraic settings. 

[10-13-22]  Wesley Calvert, SIUC

Title: Almost-sure Computable Structure Theory

Abstract: Novikov and Boone independently proved that there are finitely presented groups in which there is no algorithm to decide whether a word in the generators is equal to the identity.  More recent work, though, has shown that in many of these cases, there is an algorithm that will decide this question for almost all words.

It is possible to generalize this analysis for other kinds of structures.  The existence of structures where the basic properties are or are not computable, or where structures are classically isomorphic, but not isomorphic by a computable function, are well known.  The present talk will describe recent joint work with Cenzer and Harizanov to explain what happens if we only ask the algorithm to be right almost always.

[9-29-22] Benjamin Hutz, Saint Louis University

Title: Automorphism Groups for Arithmetic Dynamical Systems

Abstract: Algebraic dynamics is the study of iteration of polynomial or rational functions. This talk focuses on endomorphisms of projective space with non-trivial automorphisms. Under the action of conjugation by the projective general linear group, we can form a moduli space of dynamical systems of a certain degree. Certain elements in these moduli spaces have non-trivial automorphisms. This is analogous to the elliptic curves with complex multiplication in the moduli space of elliptic curves. These special maps have connections to many problems in arithmetic dynamics. We focus on two problems: identifying the locus of maps with non-trivial automorphisms and the realizability of subgroups of the projective linear group as automorphism groups.

[9-15-22] Mathew Gluck, SIUC

Title: INFINITELY MANY SIGN-CHANGING SOLUTIONS TO A CONFORMALLY INVARIANT INTEGRAL EQUATION

Abstract: Click here

[11-18-21] Kim Klinger-Logan, Rutgers University/Kansas State University (virtual)

Title: Two applications of solutions to differential equations in automorphic forms

Abstract: Automorphic forms were first studied in the context of number theory. Among their many interesting features, they give rise to $L$-functions (functions with similar properties to the Riemann zeta function). We will discuss the use of spectral theory of automorphic forms to solve differential equations and discuss two applications of such solutions.  The first application may shed light on the location of zeros of $L$-functions. The equation in question arises from mistake that allowed for zeros of the Riemann zeta function to appear as eigenvalues for the $SL_2(\mathbb{R})$ - invariant Laplace-Beltrami operator on the Poincare upper half plane and has been studied by Bombieri and Garrett.  The second application provides makes steps towards a quantum correction in the discrepancy between general relativity and empirical data. Specifically, Green, Russo and Vanhove discovered that the low energy expansion of scattering amplitude for gravitons (hypothetical particles of gravity represented by massless string states) has coefficients which satisfy differential equations in automorphic forms. We will discuss how spectral theory of automorphic forms can be used in both of these contexts.

[11-4-21] Roshini Gallage, Southern Illinois University (virtual)

Title: Numerical Approximation of Nonlinear Stochastic Differential Equations with Continuously Distributed Delay

Abstract: Stochastic delay differential equations (SDDEs) are systems of differential equations with a time lag in a noisy or random environment. Much research has been done using discrete delay where the dynamics of a process at time t depend on the state of the process in the past after a single fixed time lag \tau. We are researching processes with continuously distributed delay which depend on weighted averages of past states over the entire time lag interval [t-\tau, t]. We show the existence of a unique solution of certain nonlinear SDDEs with continuously distributed delay under local Lipschitz and generalized Khasminskii-type conditions. Further, we show that Euler-Maruyama numerical approximations of such nonlinear SDDEs converge in probability to their exact solutions. 

Joint work with Dr. Harry Randolph Hughes.

[10-21-21] Layla Sorkatti, Visitor at School of Math&Stat Sciences SIUC, University of Khartoum/Al-Neelain University (virtual)

Title: Nilpotent Symplectic Alternating Algebras

Abstract: Let F be a field. A Symplectic alternating algebra over F is a triple (V, ( , ), · ) where V is a symplectic vector space over F with respect to a non-degenerate alternating form ( , ) and · is an alternating bilinear and binary operation on V such that the law (u · v, w) = (v · w, u) holds. These algebraic structures have arisen from the study of 2-Engel groups but seem also to be of interest in their own right with many beautiful properties. We will give an overview with a focus on some recent work on the structure of nilpotent symplectic alternating algebras.

[10-14-21] Tian An Wong, University of Michigan-Dearborn (virtual)

Title: Prehomogeneous vector spaces and the Arthur-Selberg trace formula

Abstract: The Arthur-Selberg trace formula is a central tool in the theory of automorphic forms, and can be viewed as a nonabelian Poisson summation formula. Prehomogeneous vector spaces on the other hand, are arithmetic objects from which certain zeta functions can be defined. In this talk, I will give a gentle introduction to these ideas, then discuss an application of the theory of prehomogeneous vector spaces to the development of the trace formula, following earlier work of W. Hoffmann and P. Chaudouard.

[10-7-21] Henry Segerman, Oklahoma State University (virtual)

Title: Artistic mathematics: truth and beauty

Abstract: I'll talk about my work in mathematical visualization: making accurate, effective, and beautiful pictures, models, and experiences of mathematical concepts. I'll discuss what it is that makes a visualization compelling, and show many examples in the medium of 3D printing, as well as some work in virtual reality and spherical video. I'll also discuss my experiences in teaching a project-based class on 3D printing for mathematics students.

[9-30-21] Aditya Potukuchi, University of Illinois Chicago (virtual)

Title: Faster algorithms for counting independent sets in regular bipartite graphs

Abstract: I will present an algorithm that takes as input a d-regular bipartite graph G, runs in time exp(O(n/d log^3 d)), and outputs w.h.p., a (1 + o(1))-approximation to the number of independent sets in G. As a by-product of the intermediate steps to this algorithm, We also obtain, for fixed d, an FPTAS to approximate the number of independent sets in d-regular bipartite ``expanding'' graphs. More than the result itself, I wil focus more on the techniques used, which combines combinatorial methods (graph containers) with statistical physics methods (abstract polymer models and cluster expansion), and mention other recent applications. I will start from the basics, and no prior knowledge of any of the topics is assumed.

Joint work with Matthew Jenssen and Will Perkins.

[9-23-21] Kwangho Choiy, Southern Illinois University (virtual)

Title: The Principle of Functoriality and Invariants

Abstract: In the framework of the principle of functoriality programmed by R. Langlands, it is of interest to seek for invariants. We shall focus on an important class of representations, discrete series, and the setting of a connected reductive algebraic group over a $p$-adic field and its closed subgroup having the same derived subgroup. This talk shall uniformize previous relevant results and discuss how to formulate some invariants.

[4-30-20]  Wesley Calvert, Mathematics, SIUC (virtual)

Title: Uniformly Knowing Isomorphisms

Abstract: Rational vector spaces of a fixed dimension are unique up to isomorphism.  Unfortunately, this isomorphism need not be simple.  Indeed, there are explicit examples of two countable infinite-dimensional vector spaces over the rationals for which no explicit formula, algorithm, or description gives an isomorphism.  Since they are isomorphic, however, there is an oracle relative to which an isomorphism is computable.

In this connection, we consider the following problem: Given any two isomorphic countable structures (e.g. vector spaces, fields, groups, graphs, etc.), compute an isomorphism between them.  Mark Nadel proved in 1974 that there is an oracle that can solve this problem, but the classification up to Turing equivalence of all such oracles remains open.  In this joint work with Johanna Franklin and Dan Turetsky, we give one characterization of these oracles, and prove something about their diversity.

[2-27-20] Chathurika Athapattu, Mathematics, SIUC

Title: Parabolically induced Banach space representations of p-adic groups

Abstract: The Langlands program, introduced by Prof.Robert Langlands (1967), is about the connection between number theory and geometry which is not highly obvious. Then he introduced local Langland conjectures as part of it. There are many different groups over many different fields for which these conjectures can be stated. The one version is p-adic Langlands correspondence. Our research project focuses on developing the theory of the p-adic Banach space representations of reductive algebraic group over non-archimedean local fields. Such representations play a fundamental role in the p-adic Langlands program.

More specifically, we study parabolically induced representations. Parabolic induction is a basic tool in representation theory. Our goal is to describe parabolically induced representations in terms of tensor products over Iwasawa modules.

[11-21-19] Wesley Calvert, Mathematics, SIUC

Title: Mathematical Logic and Probability

Abstract: In the late 19th and early 20th centuries, logic and probability were frequently treated as closely related disciplines.  Each has, in an important sense, gone its own way, so that neither, in its modern form, is in any proper sense a systematization of the ``Laws of Thought,'' as Boole called them.

However, the last four decades have seen a remarkable rapproachment.  Algorithmic randomness has become central to computability, machine learning has become deeply entangled with model-theoretic notions of independence, and the study of random combinatorial objects and zero-one laws has arisen as a major area in neostability.

The present talk will survey some parts of the new nexus of probability and logic, along with some open questions.

[11-7-19] Greg Budzban, Dean of the College of Arts and Sciences, SIUE 

Title: Convergence conditions for non-homogeneous Markov chains via random walks on groups and semigroups

Abstract: Probability on algebraic structures provides a set of techniques that can be used to analyze non-homogeneous Markov chains.  This talk will discuss the correspondence between the two areas and provide examples of verifiable sufficient conditions, based only on the entries of the transition matrices, for the convergence of a class of non-homogeneous Markov chains.  The talk will conclude with a discussion of some open problems in the field.

[10-10-19] Bogdan Petrenko, Mathematics and Computer Science, Eastern Illinois University 

Title: The smallest number of generators and densities of generating sets of an algebra finite over the integers

Abstract: Let A be a ring whose additive group is free Abelian of finite rank. The topic of this talk is the following question: what is the probability that several random elements of A generate it as a ring? After making this question precise we will see that the answer which can be interpreted as a local-global principle. Some applications will be discussed, for example:

• What is the smallest number of generators of the direct product of 769 copies of the ring of integral 3-by-3 matrices? (Answer:  3; it is 2 for the product of 768 copies though).

• What  is  the  probability  that  2  random  3-by-3  matrices  generate the ring of integral 3-by-3 matrices: (Answer: 1/{\zeta(2)^2 \zeta(3)}, where \zeta(s) is the Riemann zeta function).

This talk will be based on my joint work with Rostyslav Kravchenko (University of Texas at Austin)  and Marcin Mazur (Binghamton University).

[9-12-19] Lingguo Bu, Curriculum and Instruction, SIUC

Title: 3D Design & Printing for Mathematics Education

Abstract: The increasingly affordable technologies of 3D design and printing provide engaging opportunities for mathematics educators to play and model mathematical ideas and structures and serve the diverse needs of students at all levels. In the context of mathematics education, the speaker reflects on his experience with 3D design and printing using design examples and further discusses pedagogical possibilities.

[9-26-19] Lakshika Gunawardarana, Mathematics, SIUC

Title: Locally Primitively Universal forms and the Primitive Counterpart of the Fifteen Theorem

Abstract: The systematic study of positive definite integral quadratic forms that represent all positive integers (or all sufficiently large positive integers) was initiated by Ramanujan a little over a century ago. Such forms are now referred to as universal (or almost universal) forms. In a groundbreaking 1917 paper, Ramanujan determined all forms of the type ax^2+by^2+cz^2+du^2 that are universal, and all those of the special type a(x^2+y^2+z^2)+du^2 that are almost universal.

In 1993, J.H. Conway and W.A. Schneeberger presented the Fifteen Theorem, which provides simple criteria to determine whether a positive definite classically integral quadratic form in any number of variables is universal. Later in 2000, M. Bhargava provided a refinement of the Fifteen Theorem and showed that there are exactly 204 positive definite classically integral quaternary quadratic forms, up to equivalence, which are universal. We try to determine which of the forms in the 204 list are primitively universal, and try to determine whether there exists a finite set S of integers such that every positive definite integral quadratic form that primitively represents the integers in S, primitively represents all positive integers. In the first half of this talk, we introduce quadratic forms in general with a brief history and present a conjecture which could be a primitive counterpart to the Fifteen Theorem. Then we review the p-adic numbers and p-adic norm and discuss their application of almost universal quadratic forms, concluding with some new results on almost primitively universal forms.

[4-25-19] Poopalasingam Sivakumar, Physics, SIUC

Title: Challenges in analyzing spectroscopic data and the potentia of machine learning to accelerate bioanalysis with spectroscopy

Abstract: Analyzing spectroscopic data can be tedious that can stretch weeks or months, depending on the sample. Especially, prompt identification of biochemical changes associated with cancer cells from spectra almost impossible using conventional spectral analysis techniques. Machine learning has the potential that could facilitate to detect minute changes in enormous spectroscopy information and to speed up the spectral analysis.

In this talk, I will discuss the application of high-resolution Raman spectroscopy to detect abnormal pancreatic cancer cells by exploiting the alteration of chemical signatures in the cells based on the vibrational signatures and address the challenges of reproducibility and replicability with Raman in bioanalysis. Raman spectroscopy provides molecular signatures and structural composition of the samples. Raman shows promising results in identifying and distinguishing biomolecules such as nucleic acids, lipids, and proteins and cells.  The spectra of cancer cells are analyzed through combinations of data-preprocessing, various dimension reduction protocols, and machine learning classification algorithms Preliminary investigation of pancreatic Mia PaCa-2 cancer cells lines versus parental cell lines based on combing spectroscopic data with machine learning techniques shows a promising result.

[4-18-19] Chathurangi Pathiravasan, Mathematics, SIUC

Title: Application of Kullback-Leibler Divergence in one-way ANOVA

Abstract:  Kullback-Liebler (KL) divergence, known as relative entropy, is a measure of difference between two probability distributions. The concept was originated in probability theory and information theory, and now widely used in different literature such as data mining, time-series analysis and Bayesian analysis. In this study, we have shown the minimization problem with KL divergence plays a vital part in one-way Analysis of Variance (ANOVA) when comparing means of different groups. As immediate generalization, a new semi-parametric approach is introduced and it can be used for both means and variance comparisons of any type of distributions. The simulation studies show that the proposed method has favorable performance than the classical one-way ANOVA. The method is demonstrated on experimental radar reflectivity data and credit limit data. Asymptotic properties of the proposed estimators are derived with the purpose of developing a new test statistic for testing equality of distributions.

Keywords: Kullback-Leibler Divergence, Analysis of Variance, Asymptotic Properties

[4-11-19] Upul Rupassara, Mathematics, SIUC

Title: Joint exit time and place distribution for Brownian motion on Riemannian manifolds and the asymptotic independence condition

Abstract:  The joint distribution of first exit time and place of Brownian motion from normal balls of sufficiently small radius is considered. The asymptotic expansion of the joint Laplace transform of exit time and spherical harmonics of exit position is derived for a ball of small radius. A generalized Pizetti's formula is used to expand the solution of the related partial differential equations. These expansions are represented in terms of curvature in the manifold. The geometric properties of Riemannian manifolds are derived in the case where the first exit time and place are statistically independent. In particular, it is proven that an Asymptotic Uncorrelated Condition (AUC) involving orders of first exit time and position equivalent to the certain level of curvature conditions depending on the level of asymptotics. Further, a generalized formula is derived for arbitrary moments of first exit time at corresponding orders of asymptotics.

[3-28-19] Jerzy Kocik, Mathematics, SIUC

Title: Spinors, geometry, and numbers

Abstract:  Spinor spaces hold representations of the orthogonal groups and "explain" the curious behavior of certain object that need to be turned twice to return to the initial state.  Quite intriguing, the same algebraic construct can be applied to configurations of circles.  We shall define a "tangency spinor" and see how it connects various aspects of geometry, topology and algebra, not to mention  visualization of otherwise mysterious properties of quantum objects. 

Keywords:  Split quaternions, Stern-Brocot tree, space-time, arithmetic functions, tessellations.

[2-28-19] Keith T. Gagnon, Biochemistry and Molecular Biology – SMC (Biochemistry & Molecular Biology, Chemistry & Biochemistry), SIUC

Title: Rational Design of Inhibitors to Safely Control CRISPR Gene-Editing Enzymes

Abstract: CRISPR is a new enzyme-based technology that can be used to precisely "edit" the genomes of living organisms. This technology is not only being developed for basic science, but also as a potential gene therapy. Although CRISPR is an exciting technology that could one day cure diseases like cancer or Alzheimer's, it is not perfect and can potentially produce unwanted side-effects. To improve the control and safety of therapeutic or technology development, inhibitors that can act as a "kill switch" to turn off the enzyme are needed. This seminar will describe CRISPR technology and the rational design of successful inhibitors based on biochemical principles. 

[2-14-19] Banafsheh Rekabdar, Computer Science, SIUC

Title: The current state of deep learning

Abstract: Deep Learning is a subset of Machine Learning which deals with deep neural networks. Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection, time-seres data analytics, safety and security, natural language processing and many other domains such as biology and genomics. 

[11-15-18] Kofi Placid Adragni, Senior Research Scientist, Eli Lilly and Company

Title: Sufficient Dimension Reduction of Features in the Presence of Dependent Observations

Abstract: Sufficient dimension reduction methods are designed to help reduce the dimensionality of large datasets without loss of regression information for a better visualization, prediction, and modeling. We develop their use for dependent multi- dimensional features with respect to an outcome of interest in the presence of other covariates. Existing likelihood-based sufficient dimension reduction methods assumes independent and identically distributed samples. However, observations are often recorded on subjects or clusters. While the observations from cluster to cluster could be independent, the within-cluster observations are likely dependent. Treating the within-cluster observations as independent may adversely affect the estimation of the central subspace. We propose a method for estimation of the central subspace when the observations are dependent within cluster and discuss some structures of the dependence among the features.

[10-25-18] John P. McSorley, Mathematics, SIUC

Title: Sequential Covering Designs

Abstract: Click here

[9-27-18] Min Li, Visitor at Department of Mathematics SIUC, ShenZhen University

Title: Schatten Quasi-Norm Induced Models for Image Decomposition, Completion and Salient Object Detection

Abstract:  Image decomposition, completion and salient object detection are not only ubiquitous but also challenging tasks in the study of computer vision. Image processing using mathematical methods has always been the trend of applied mathematics. In recent years, the latest research hotspot is the matrix rank minimization problem which arises in a wide range of applications. Inspired by this, we firstly propose a novel regularization model for image decomposition and data completion, which integrates relative total variation (RTV) with Schatten-1/2 or Schatten-2/3 norm, respectively. Secondly, we give salient object detection based on weighted group sparsity and Schatten-1 or Schatten-2/3 or Schatten-1/2 norm. The proposed model is in essence divided into ”regularization term+double nuclear norm” and ”regularization term+ Frobenius/nuclear hybrid norm”, which can be solved by splitting variables and then by using the alternating direction method of multiplier (ADMM). Meanwhile, Convergence of the algorithm is discussed in detail.

[9-13-18] Kwangho Choiy, Mathematics, SIUC

Title: Some arithmetic objects in discrete series representations of p-adic groups

Abstract: Studying some classes of representations of a p-adic group, we encounter some interesting arithmetic objects in it. In this talk, we shall focus on discrete series representations that are simply related to L2-space, introduce some arithmetic objects including their multiplicities in the restriction and formal degrees. We also discuss their connections to the local Langlands correspondence of p-adic groups. 

**This talk will begin with basic concepts and backgrounds that are accessible to undergraduate and early-year graduate students.   

SALAH MOHAMMAD MEMORIAL COLLOQUIUM SERIES

[11-16-17] Zoi Rapti, Mathematics, UIUC

Title: Direct and Indirect Effects of Species Interactions in Disease Systems

Abstract: Indirect effects, both density- and trait-mediated, have been known to act in tandem with direct effects in the interactions of numerous species. They have been shown to affect populations embedded in competitive and mutualistic networks alike. At the same time, in disease systems, pathogens can harm their hosts in a variety of ways. For this reason, we define virulence as an umbrella term that encompasses disease induced mortality, fecundity reduction and increased predation due to the disease. Moreover, competitors can alter the course of an epidemic through disease dilution or amplification. All these interactions greatly complicate the task of determining key factors and interactions in disease spread.

In this talk, we will introduce mathematical models based on coupled ordinary and partial differential equations to investigate the invasibility and prevalence of an obligately killing fungal parasite in a zooplankton host as they are embedded in a complex ecological network of predators, competitors and resources. Among our main findings is the demonstration that indirect effects cause qualitative and quantitative changes almost indistinguishable from direct effects and the theoretical verification of the fact that the effects of direct and indirect mechanisms cannot be disentangled. Our results underpin the conclusions of past studies calling for comprehensive models that incorporate both direct and indirect effects to better describe field data. We also demonstrate trade-offs among the various manifestations of virulence and how these together with life-history traits shape the disease dynamics.

This is joint work with C. Caceres, T. Stewart, J. Kavouras, and B.Mueller-Brennan.   

SALAH MOHAMMAD MEMORIAL COLLOQUIUM SERIES

[11-9-17] Anna Haensch, Mathematics and Computer Science, DuQuesne University

Title: Almost universal ternary sums of polygonal numbers

Abstract:  In 1796 Gauss showed that every natural number can be written as the sum of three triangular numbers. In 2009, Chan and Oh determined when a weighted sum of triangular numbers (i.e. triangular numbers with coefficients) represents all but finitely many natural numbers. We say such a sum is almost universal. In this talk we will determine when a sum of three generalized m-gonal numbers is almost universal. We will approach this question first from an algebraic, and then from analytic point of view, exploiting the capabilities of each method, and realizing new connections between the machinery.

SALAH MOHAMMAD MEMORIAL COLLOQUIUM SERIES

[10-26-17] Yaser Samadi, Mathematics, SIUC

Title: Factor model for matrix and tensor time series data

Abstract:  Many data sets from across the sciences collect sequences of matrix- and tensor-structured data; we refer to such data as tensor time series.  To explore and highlight the main dynamic structure of a set of multivariate time series, we extend the use of standard variance-covariance matrices for non-time series data in principal component analysis. This is also  achieved by combining the principles of both canonical correlation analysis and principal component analysis for time series to obtain a new type of covariance/correlation matrix for a principal component analysis to produce a so-called “principal component time series”.

Another application, we are particularly motivated by electrophysiology studies in which electrical activity at multiple locations in the brain is measured over time. it is typical to pre-process such data to obtain tensors for each short time interval representing the level of coherence between each pair of brain regions at each spectral frequency.   We propose a flexible class of nonparametric factor models for  tensor time series data, which reduce dimensionality and maintain interpretability through the incorporation of sparsity constraints. The ability to accurately infer dynamically changing subnetworks is shown through simulations, and the methods are applied to mouse electrophysiology data.

SALAH MOHAMMAD MEMORIAL COLLOQUIUM SERIES

[10-19-17] Wesley Calvert, Mathematics, SIUC

Title: Almost

Abstract: For some problems in mathematics, we have algorithms.  For others, we have none.  Often, the proof of non-existence of an algorithm can feel severely contrived, so that the proof is unsatisfying --- we'd have to get fabulously unlucky where the algorithm fails.  The worst-case complexity of the simplex method is horrible — if we encounter such an exotic example as to be in the worst case --- yet it runs without serious inconvenience every day.

What happens if, instead of asking for an algorithm that always works, we ask for one that works for everything except a very small set of pathological examples?  Come and see.

SALAH MOHAMMAD MEMORIAL COLLOQUIUM SERIES

[9-28-17] Eric Chitamber, Physics, SIUC       

Speaker's website:

Title: Transforming Resources within a Quantum Resource Theory

Abstract: A quantum resource theory studies what physical processes are possible when constraints are placed on an experimenter’s operational capabilities.  Under these restrictions, certain states become impossible to create, thereby rendering them as a “resource” for quantum information processing.  The paradigm example of a quantum resource is entanglement, which cannot be generated by multiple experiments located in spatially separated laboratories.

In this talk I will discuss the mathematical structure of a general quantum resource theory and describe typical problems encountered.  In particular, I will discuss the problem of resource transformation, which asks whether or not one state can be converted to another under the allowed operations of the theory.  Recent work on the subject will be presented.

SALAH MOHAMMAD MEMORIAL COLLOQUIUM SERIES

[9-14-17] Matthias Strauch, Mathematics, Indiana University, Bloomington

Title:  Functions On a Covering for the P-adic Upper Half Plane

Abstract: The Poincare upper half plane of complex numbers with positive imaginary part is an important source of representations of the group SL(2,R) which acts on it by Moebius transformations. In the world of p-adic numbers there is a space which plays an analogous role, the so-called p-adic upper half plane. Interestingly, whereas the Poincare upper half plane is simply connected, the p-adic upper half plane carries a whole tower of equivariant covering spaces. In this talk I will first explain the geometry of one particular of these covering spaces, following work by J. Teitelbaum. Secondly, I will discuss a method for analyzing the space of functions on this covering as a representation. This is joint work with Deepam Patel and Tobias Schmidt.

[4-27-17] Hasthika Rupasinghe, Mathematics, SIUC

Title: Bootstrapping Analogs of the One Way Manova Test

Abstract: The classical one way MANOVA model is used to test whether the mean measurements are the same or differ across p groups, and assumes that the covariance matrix of each group is the same. This work suggests using the Olive (2017abc) bootstrap technique to develop analogs of one way MANOVA test. A large sample theory test has also been developed. The bootstrap  tests can have considerable outlier resistance, and the tests do not need the population covariance matrices to be equal. The two sample Hotelling's  T^2 test is the special case of the one way MANOVA model when p =2.

[4-20-17] Nabendu Pal, Mathematics, University of Louisiana at Lafayette

Title: Analysis of Non-Negative Observations Subject to Two Factors Using Gamma Models

Abstract: A two-factor analysis of variance (ANOVA) is widely used in design of experiments when experimental units are subjected to two factors (i.e., potential sources of variations). However, such an analysis, which uses the F-tests, is dependent on three critical assumptions, - (i) all the main and interaction effects as well as the unexplained error term are additive to explain the response variable; (ii) the errors are all independent and follow a normal distribution; and (iii) the error variances, though unknown, are all equal (i.e., the errors are homoscedastic). In many engineering and biological studies, where the observations are non-negative to begin with, it is often found that one or more of the above assumptions is/are not tenable. Further, the observations tend to exhibit positively skewed distributions as seen from sample histograms. In such situations, the standard operating procedure (SOP) of the two-factor ANOVA calls for a suitable (Box-Cox type) transformation, so that the transformed observations can follow the aforementioned model assumptions. There are two practical difficulties faced by the researchers with the transformed observations: (a) the transformed observations lose their relevance to the original problem, and the resultant unit(s) of the transformed observations can be meaningless, and (b) it becomes a subjective call to come up with the most appropriate transformation of the data, i.e., one transformation can make the data adhere to one assumption while another transformation can make the data follow another assumption closely. Faced with such a dilemma we offer a completely new paradigm where the non-negative observations, influenced by two factors, are modeled by gamma distributions with unknown shape and scale parameters which are dependent on the corresponding factor levels. We then proceed with testing the main effects (whether the main effects of a factor are all equal or not) and interaction effects (whether the interactions exist or not). To test a null hypothesis against a suitable alternative, we first derive the likelihood ratio test (LRT) based on its asymptotic Chi-square distribution. But since the asymptotic LRT (henceforth called 'ALRT') may not work well for small to moderate sample sizes we then propose a parametric bootstrap (PB) test based on the LRT statistic which does not use the Chi-square distribution, rather finds its critical value automatically through simulation. The PB test using LRT statistic (henceforth called 'PBLRT') appears to work very well in terms of maintaining the nominal level as seen from our comprehensive simulation study. Further, we present some real-life datasets to buttress the applicability of our proposed PBLRT over the classical ALRT, and to show how the inferences may differ from the ones based on traditional ANOVA.

[4-13-17] Shiva Houshmand, Computer Science, SIUC

Title: Modern Techniques in Password Cracking and Password Meters

Abstract: Passwords are critical for security in many different domains such as social networks, emails, encryption of sensitive data and online banking. Human memorable passwords are thus a key element in the security of such systems. It is important for system administrators to have access to the most powerful and efficient attacks to assess the security of their systems more accurately. In this talk I describe the recent techniques for password cracking and assessing the strength of passwords. The probabilistic context-free grammar technique has been shown to be very effective in password cracking. In this approach, the system is trained on a set of revealed passwords and a probabilistic context-free grammar is constructed. The grammar is then used to generate guesses in highest probability order, which is the optimal off-line attack. I also describe how entropy measures and Markov models have been used as password-strength meters to analyze the strength of user chosen passwords. A new password meter will also be introduced that estimates the probability of passwords being cracked. The system modifies the weak password slightly and suggests a new stronger password to the user. By dynamically updating the grammar we make sure that the guessing entropy increases and the suggested passwords thus remain resistant to various attacks.

[3-30-17] Aaron Luttman, Manager, Diagnostic Research and Material Studies, Nevada National Security Site

Title: Quantifying Uncertainties in Inverse Problems: Meaning and Usefulness of Error Bars in Large-Scale Inversion 

Abstract: While the U.S. Department of Energy’s National Nuclear Security Administration (NNSA) has moved to a scientific paradigm driven by modeling and simulation and in which experimentation is motivated primarily by code validation, there is still much to be learned by analyzing data directly and extracting information from experimental data by solving inverse problems. In order to quantify the uncertainties associated with the solutions, however, it is necessary to use statistical approaches to formulating the inverse problems and to understand the nature of the uncertainties for which such formulations can correctly account. In this work we will present data from NNSA X-ray imaging experiments related to the stockpile stewardship program, some inverse problems whose solutions inform the evolution of our experiments and diagnostics systems, and the challenges associated with the Bayesian formalisms used to assign error bars to the information extracted. The discussion will include details of the experiments themselves, where mathematical data analysts fit into the experimental programs, the role of mathematical theory in development of analysis techniques, and results demonstrating the efficacy of solving statistical inverse problems to drive stockpile stewardship.

[2-23-17] Kwangho Choiy, Mathematics, SIUC

Title: Finite Group Theory and Local Langlands Conjecture

Abstract: The local Langlands conjecture for p-adic groups partitions the infinite set of equivalence classes of irreducible smooth complex representations of the p-adic groups into finite subsets whose internal structures are conjecturally interpreted in terms of irreducible representations of certain finite groups (Sgroups). As a part of the local Langlands conjecture, decompositions of tempered parabolic inductions into irreducible constituents are governed by certain finite groups (R-groups). In this context, we shall discuss various roles of finite group theory in the far-reaching local Langlands conjecture for p-adic groups.

[12-1-16] Mehmet Gumus, Mathematics, SIUC

Title: Some New Results on Lyapunov-Type Diagonal Stability

Abstract:  In this talk, we present several recent developments regarding Lyapunov diag-onal stability. This type of matrix stability plays an important role in various applied areas such as population dynamics, systems theory, complex networks, and mathematical economics. First, we establish a necessary and sufficient condition, based on the Schur complement, for determining Lyapunov diagonal stability of a matrix. This condition reduces the problem to common diagonal Lyapunov solutions on two matrices of order one less. We develop a number of extensions to this result, and formulate the range of feasible diagonal Lya-punov solutions. In particular, we derive explicit algebraic conditions for a set of 2 × 2 matrices to share a common diagonal Lyapunov solution. Second, the connection between Lyapunov diagonal stability and P -matrix property under Hadamard multiplication is extended. We present a new characterization involv-ing Hadamard multiplications for simultaneous Lyapunov diagonal stability on a set of matrices. This development is based upon a recent result concerning si-multaneous Lyapunov diagonal stability and a new concept called P-sets, which is a generalization of P -matrices. Third, we consider various types of matrix sta-bility involving a partition α of {1, . . . , n}. We introduce the notions of additive H(α)-stability and P0(α)-matrices, extending those of additive D-stability and nonsingular P0-matrices. Several new results are developed, connecting additive H(α)-stability and the P0(α)-matrix property to the existing results on matrix stability involving α. The extensions of results related to Lyapunov diagonal stability, D-stability, and additive D-stability are discussed.

[11-17-16] Mahtab Hajebi, Visitor at Department of Mathematics, SIUC

Title: A Semiparametric Method for Estimating Nonlinear and Partial Linear Vector Autoregressive Time Series Models with Independent and Dependent Errors

Abstract: Abstract: A semiparametric method is proposed to estimate vector autoregressive function in the nonlinear and partially linear vector time series model. We consider a combination of parametric and nonparametric estimation approach to estimate the nonlinear vector autoregressive function for both independent and dependent errors. The multivariate Taylor series expansion is utilized to approximate the vector regression function up to the second order. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained nonlinear vector autoregressive function is adjusted by a nonparametric diagonal matrix. The proposed adjusted matrix is estimated using nonparametric kernel method.

Asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. Finally, we demonstrate the application of the proposed approach with an empirical example.

[11-10-16] Jennifer Koran, Counseling, Quantitative Methods, and Special Education, SIUC

Title: The Multivariate Percentile Power Method Transformation

Abstract: The conventional power method transformation is a moment-matching technique that simulates non-normal distributions with controlled measures of skew and kurtosis. The percentile power method transformation is an alternative that uses the percentiles of a distribution in lieu of moments. This presentation covers the multivariate percentile power method transformation, which is used to simultaneously simulate several non-normal variates using percentiles and a specified correlation matrix. Empirical illustrations are provided, including demonstration of the percentile power method transformation using a publicly-available SAS macro. The macro and instructions for using it can be found at https://digitalcommons.wayne.edu/jmasm/vol15/iss1/42. 

Math SIUC - Art, Math and Science: An Interdisciplinary Colloquium

[10-20-16] Marie Bukowski, School of Art and Design, SIUC

Title: Art and Mathematical Instinct: The Relationship Between Art and Math

Abstract:  I believe that art making is a pioneering, transformative act that moves, often changes, and sometimes revolutionizes culture.  To achieve this, I have become more aware, reflective, and adept, willing to expand skills and capacities and to place my own work within a creative inquiry that takes me more deeply into the nature and meaning of my work.  I incorporate diverse, interdisciplinary perspectives into my art practice, and use them to create art that is truly innovative, has deep impact, or powerfully challenges personal or cultural perceptions.  I cross disciplines by working with practicing scientists and researchers so that our journeys are enriched by multiple perspectives and disciplines. Art & the Mathemaical Instinct will discuss the influence that mathematical and scientific events have had on my creative research.

Click here to visit Marie Bukowski's website

[10-6-16] Andrew Earnest, Mathematics, SIUC

Title: Integral Quadratic Forms and Lattices Satisfying Regularity Conditions

Abstract:  In 1927, L.E. Dickson introduced the term ‘regular' to refer to a positive definite ternary integral quadratic form with the property that it represents all the positive integers not ruled out for representation by congruence conditions. In more modern terminology, the regular forms are those for which a local-global principle holds for the representation of integers. Since that time, quadratic forms and lattices with this property and various natural generalizations of it have been studied extensively. In this talk, we will give an overview of some of the main results that have been obtained, describe some recent advances, and indicate some remaining open problems on these interesting classes of lattices.

[9-22-16] H.R. Hughes, Mathematics, SIUC

Title: A Variational Approach to Stochastic Problems

Abstract:  A relationship between optimal control and calculus of variations problems is exploited to investigate variational formulations of several stochastic problems, including Brownian bridge and the stochastic linear regulator problem. Computational approaches are presented.

[9-8-16] Daniel Spector, Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan

Title: Taylor Approximations and Sobolev Spaces

Abstract:  In this talk we will introduce the sometimes difficult to understand Sobolev spaces as a simple extension of the Taylor approximation of classically differentiable functions (C1).