# Colloquia

## 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

## Yongwei Yao

Lech’s inequality, the Stuckrad-Vogel conjecture, and uniform behavior of Koszul homology

Date: 8/17/2018

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

**Abstract** : View

All are welcome.

## Tokuji Araya

An introduction to the Path Algebras

Date: 8/16/2018

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

**Abstract**: View

All are welcome.

## Hehui Wu

Vertex Partition with Average Degree Constraint

Date: 5/31/2018

Time: 3:00PM-4:00PM

Place: 315 Armstrong Hall

**Abstract**: A classical result, due to Stiebitz in 1996, states that a graph with minimum degree $s+t+1$ contains a vertex partition $(A, B)$, such that $G[A]$ has minimum degree at least $s$ and $G[B]$ has minimum degree at least $t$. Motivated by this result, it was conjectured that for any non- negative real number s and t, such that if G is a non-null graph with average degree at least $s + t + 2$, then there exist a vertex partition $(A, B)$ such that $G[A]$ has average degree at least $s$ and $G[B]$ has average degree at least $t$. Earlier, we claimed a weaker result of the conjecture that there exist two disjoint vertex set $A$ and $B$ (for which the union may not be all the vertices) that satisfy the required average degree constraints. Very recently, we fully proved the conjecture. This is joint work with Yan Wang at Facebook.

All are welcome.

## Xiaoya Zha

Non-revisiting Paths in Polyhedral Maps on Surfaces

Date: 4/27/2018

Time: 3:30PM-4:30PM

Place: 315 Armstrong Hall

**Abstract**: The Non-revisiting Path Conjecture (or Wv-path Conjecture) due to Klee and Wolfe states that any two vertices of a simple polytope can be joined by a path that does not revisit any facet. This is equivalent to the well-known Hirsch Conjecture. Klee conjectured even more, namely that the Non-revisiting Path Conjecture is true for all general cell complexes. Klee proved that the Non-revisiting Path Conjecture is true for 3-polytope (3-connected plane graphs). Later, the general Non-revisiting Path Conjecture was varied for polyhedral maps on the projective plane and the torus by Barnette, and on the Klein bottle by Pulapaka and Vince. However, a few years ago, Santos proved that the Hirsch conjecture is false in general.

In this talk, we show that the the non-revisiting path problem is closely related to

(i) the local connectivity $\kappa_G(x; y)$ (i.e. the number of disjoint paths between x and y);

(ii) the number of dfferent homotopy classes of (x; y)-paths;

(iii) the number of (x; y)-paths in each homotopy class.

For a given surface $\Sigma$, we give quantitative conditions for the existence of non-revisiting paths between x and y. We also provide more systematic counterexamples with high number (linear to genus of the surface) of paths between x and y but without any non-revisiting path between them. These results show the importance of topological properties of embeddings of underline graphs for this geometric setting problem.

This is joint work with Michael Plummer and Dong Ye.

This talk will be accessible to graduate students.

All are welcome.

## Xiangwen Li

Every planar graph without adjacent cycles of length at most 8 is 3-choosable.

Date: 4/26/2018

Time: 3:30PM-4:30PM

Place: 315 Armstrong Hall

**Abstract**: DP-coloring as a generation of list coloring was introduced by Dvovrak and Postle in 2017,

who proved that every planar graph without cycles from 4 to 8 is 3-choosable, which was conjectured by Brodian et al. in 2007. In this paper, we prove that every planar graph without adjacent cycles of length at most 8 is 3-choosable, which extends this result of Dvovrak and Postle.

This talk will be accessible to graduate students.

All are welcome.

## Liming Xiong

Fobidden subgraphs, some propertices: Hamiltonicity and Superieulerian in graphs

Date: 4/26/2018

Time: 4:30PM-5:30PM

Place: 315 Armstrong Hall

**Abstract**: In this talk, we persent some results between forbidden pair of subgraphs and supereuleriancity and hamiltoncity, by using the characterization of supereuleriancity by induced minor, obtained in [Lai, Supereulerian graphs and excluded induced minors, Discrete Math. 146(1995)], we present results on a complete characterizations of the existence of spanning eulerian subgraph, the similar problem for 2-factors is also considered.

This talk will be accessible to graduate students.

All are welcome.

## Robin Baidya

Six ways to compare modules

Date: 4/24/2018

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

**Abstract**: How many copies of one object exist in another? How many copies of one object are required to build another? If we can build an object using a particular method, to what extent is that method unique? These questions pervade mathematics, and they must be interpreted diﬀerently in diﬀerent contexts. We will approach these questions as they pertain to modules. To answer the ﬁrst question, we will study how modules embed and factor. For the second question, we will consider the various ways through which a module can be generated and cogenerated. We will investigate the question of uniqueness as it applies to the splitting of modules and to the problem of cancellation. By the end of the talk, we will have covered two ways to interpret each of our three questions, yielding six ways to compare modules.

This talk will be accessible to graduate students.

All are welcome.

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