# Colloquia

## Jocelyn Quaintance

Hilbert Spaces, Hilbert Bases, and Fourier Series

**Date:** 11/14/2018

**Time:** 4:00PM-5:00PM

**Place:** 315 Armstrong Hall

**Abstract: **In honor of Salah Hamad's dissertation defense, I will give a graduate student accessible

talk discussing the basic theory of Hilbert spaces. In particular, I will define what it means for a Hilbert space

$E$ to have a Hilbert basis $(u_k)_{k\in K}$ and show how the concept of a Hilbert basis provides the canonical representation

of $E$ in terms of $l^2(K)$, namely the famous Riesz-Fischer theorem. Then I will discuss the connection between Hilbert bases and

the Fourier series of a square period function, ending with a brief recap of Joseph Fourier's fascinating life.

## Dong Ye

Cyclability and Linkage for Graphs with Local Conditions

Date: 11/9/2018

Time: 3:30PM-4:30PM

Place: 315 Armstrong Hall

**Abstract**: A graph G is k-cyclable if for any given k vertices, G has a cycle through all the given k vertices. It is well known that a k-connected graph is k-cyclable. A graph G is k-ordered or C_k-linked if for any give k vertices in an ordering, G has a cycle through all the given k vertices in the ordering. More general, a graph in H-linked if there is a injective map f which maps vertices of H to G such that G has a subgraph homeomorphic to H and rooted at f(V(H)). In this talk, we present some results on cyclability and linkage for graphs with extra local conditions, such as, claw-free and locally Hamiltonian etc.

All are welcome.

## William "Bus" Jaco

Student Learning and Success in Entry-level Mathematics: Math Pathways, Corequisite Instruction, and Mathematics Learning by Inquiry

**Date:** 11/09/2018**Time:** 3:30PM-4:30PM**Place:** 121 Armstrong Hall

**Abstract: **We will facilitate a discussion of the program led by the Oklahoma State Regents for Higher Education to enhance student learning and success in mathematics across Oklahoma. We will discuss the structures of Math Pathways (to Completion) and Corequisite Instruction (at Scale) that are being implemented at all public institutions of higher education across Oklahoma, taking a closer look at these structural changes at OSU. While these structural changes are not easy, they are fairly straightforward and from them we are seeing measurable successes. However, a consequence of these changes and the need to address the Task Force Goals for enhanced student engagement, increased applications of mathematics and support for academic success skills dictate necessary classroom instructional changes that will require a shift in departmental culture and faculty and advisor professional development. The newly funded Mathematics Inquiry Project is a statewide program to address these challenging changes.

## Mingquan Zhan

On s-hamiltonian-connected line graphs

Date: 10/25/2018

Time: 3:45PM-4:45PM

Place: 315 Armstrong Hall

**Abstract**: View

All are welcome.

## Liang Hong

On prediction of future insurance claims when the model is uncertain

Date: 10/19/2018

Time: 3:30PM-4:30PM

Place: 315 Armstrong Hall

**Abstract**: Predictive modeling is arguably one of the most important tasks actuaries face in their day-to-day work. In practice, actuaries may have a number of reasonable models to consider, all of which will provide different predictions. The most common strategy is to first use some kind of model selection tool to select a ``best model,'' and then use that model to make predictions. However, there is reason to be concerned about the use of the classical distribution theory to develop predictions because these ignore the selection effect. Since accuracy of predictions is crucial to the insurer's pricing and solvency, care is needed to develop valid prediction methods. In this talk, we undertake an investigation of the effects of model selection on the validity of classical prediction tools and make some recommendations for practitioners.

Dr. Hong received his PhD in mathematics from Purdue University. He has received grants from the Casualty Actuarial Society (CAS), Society of Actuaries (SOA), and State Farm Insurance Company; and he has given research talks at several Center for Actuarial Excellence (CAE) schools including Drake University, Georgia State University, Temple University, University of Waterloo, University of Wisconsin, Madison.

All are welcome.

## Zhi-Hong Chen

Degree conditions on induced nets for the hamiltonicity of claw-free graphs

Date: 10/11/2018

Time: 3:45PM-4:45PM

Place: 315 Armstrong Hall

**Abstract**: View

All are welcome.

## Xiaofeng Gu

Packing spanning 2-connected subgraphs and spanning trees

Date: 10/05/2018

Time: 3:30PM-4:30PM

Place: 120 Armstrong Hall

**Abstract**:

Motivated by the well known spanning tree packing theorem by Nash-Williams and Tutte, we discover a suﬃcient partition condition of packing spanning 2-connected subgraphs and spanning trees. As a corollary, it is shown that every (4k+2l)-connected and essentially (6k +2l)-connected graph contains k spanning 2-connected subgraphs and l spanning trees that are pairwise edge-disjoint. Utilizing it, we show that every 6-connected and essentially 8-connected graph G contains a spanning tree T such that G−E(T) is 2-connected.

All are welcome.

## Dana Tudorascu

Technical Challenges in the Analysis of Alzheimer's Disease Brain

Date: 10/04/2018

Time: 3:45PM-4:45PM

Place: 315 Armstrong Hall

**Abstract**: View

All are welcome.

## Jugal Verma

Milnor numbers of hypersurface singularities, mixed multiplicities of ideals and volumes of polytopes

Date: 9/20/2018

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

**Abstract**: View

If $H$ is an analytic surface defined by $f=0$ in $\mathbb C^{n+1}$ with an isolated singularity at the origin, then the colength of the Jacobian ideal $J(f)$ is called its Milnor number. B. Teissier refined this notion to a sequence of $\mu^*(H)$ Milnor numbers of intersections of $H$ with general linear spaces of dimension $i$ for $i=0,1,\dots, (n+1).$ J. J. Risler and Teissier showed that this sequence coincides with the mixed multiplicities of the maximal ideal and $J(f).$ They proposed conjectures about log-convexity of the $\mu^*(H)$ which were solved by B. Teissier, D. Rees-R. Y. Sharp and D. Katz. These give rise to Minkowski inequality and equality for the Hilbert-Samuel multiplicities of ideals. Mixed multiplicities are also connected with volumes of polytopes and hence to counting solutions to polynomial equations.

All are welcome.

## Bill Kazmierczak

Dr. Kazmierczak is the Calculus Coordinator at Binghamton and recently implemented "split" calculus. This means that Calculus 1 and Calculus 2 are each taught in two half semester courses, and students can drop/add midsemester courses as needed. Calculus 2A material covers integration techniques and applications, and Calculus 2B covers sequences, series, and polar coordinates. If a student starts the semester in Calculus 2A and passes, then he/she could continue on to Calculus 2B in the second half of the semester. However, if the student doesn't pass, then he/she could start Calculus 2A again during the second half of the semester and would take Calculus 2B the next semester.

We have been discussing the possibility of implementing this type of system for our calculus courses at WVU and would like to learn about Dr. Kazmierczak's experience at Binghamton University.

Please join us for the colloquium, and feel free to share this e-mail with anyone who might be interested.

Date: 09/19/2018

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

## Pages