# Spring 2016 – Algebra and Discrete Math (ADM) Seminar

## Spring 2016

#### Thursdays 3:30-4:30 – Room M-102

Organizers:
Felice Manganiello (manganm@clemson.edu)
Gretchen L. Matthews (gmatthe@clemson.edu)

Date Talk
Jan. 21
• ## Phan Thanh Toan - Pohang University of Science and Technology

Some results on error-correcting codes
Let A(n,d) (resp. A(n,d,w)) be the maximum possible number of codewords in a binary code (resp. binary constant-weight w code) of length n and minimum Hamming distance at least d. The problem of determining the values of A(n,d) and A(n,d,w) is a fundamental problem in coding theory. The cases when n \leq 28 attract most attention in the research community. For unknown values of A(n,d) and A(n,d,w), several works have been done to locate them by giving lower and upper bounds. While lower bounds are obtained from explicit code constructions, upper bounds involve analytic methods. In this talk, we will present some of our results that give new upper bounds on A(n,d) and A(n,d,w). A survey on lower bounds will be discussed.
Mar. 3
• ## Lance Miller - University of Arkansas

F-invariants and determinants
This talk will survey important themes in the study of positive characteristic singular varieties. Notably, many important questions concern certain discrete "invariants" which are easily defined; some of which have surprisingly deep connections across areas as divers as complex analysis, complex algebraic geometry, commutative algebra, and number theory. Towards the end, we'll focus on varieties defined by determinants and survey some new results as well as some open questions.
Mar. 10
• ## COLLOQUIUM - Amnon J. Meir - South Methodist University

A Rotator's View of the NSF:
Everything You Ever Wanted To Know About The NSF (But Were Afraid To Ask)
During the first part of the talk I will provide an overview of the NSF and, in particular, MPS/DMS from the perspective of a faculty rotator. I will also describe proposal handling (by the NSF), the merit review process, and suggest some "dos and don'ts" when preparing and submitting a proposal. I will devote the second part of the talk to answering your questions about the NSF, DMS, and the review process (even those you were/are afraid to ask, so please come prepared).
Mar. 24
• ## Sean Sather-Wagstaff - Clemson University

Interactions between Algebra and Topology: Homology and Support
In this talk, I will discuss some of the (many) ways that algebraists use topological techniques to solve algebraic problems. This story actually begins with ways that topologists use algebraic techniques to solve topological problems. The presentation will be very colloquial, in particular, it will be accessible to graduate students.
Apr. 1 Friday
• ## Elena Dimitrova - Clemson University

Properties and applications of vanishing ideals of points over finite fields.
The easiest geometric object to compute over affine or projective space is a single point. It has no secrets -- in particular, its defining ideal, the set of polynomials which vanish at the point, is straightforward to describe. In contrast, vanishing ideals of multiple points is a challenge even over a finite field. Though efficient techniques for computing them, such as the BM-algorithm, exist, for most sets of points the vanishing ideal has several equally nice" generating sets which yield multiple interpolating polynomials.In this talk, we will explore properties of vanishing ideals, particularly over finite fields. Additionally, we will see how these questions arise naturally in the design of experiments and selection of algebraic models of systems in mathematical biology.
Apr. 7
• ## Anne Ho - Coastal Carolina University

Orb Family Mischief (aka How to Count Artin-Schreier Curves)
Once upon a time, there lived a family of orbs with four children.  Of these children, the oldest three were identical triplets.  Being a mischievous trio, they liked to confuse neighbors, schoolteachers, and strangers alike as to who was who.  In this talk, I will relate the story of the Orb family and how they are tied to my research (which is on counting Artin-Schreier curves over finite fields).
Apr. 21
• ## Steve Szabo - Eastern Kentucky University

Size Condition on Codes over Rings and Some Duality Preserving Grey Maps
Consider a finite Frobenius ring A and an n-length left A-linear code C with C' its Euclidean right dual. In this talk we will show that the size condition given by Jay Wood in 1999 that |C|*|C'|=|A|^n holds when considering duality defined more generally on any non-degenerate form. Also, given a finite Frobenius ring A which is a free left module over a subring R of A, we will discuss two types of R-bases which are used to defined duality preserving maps from codes over A to codes over R.