TEXAS A&M UNIVERSITY - FALL 2019
Graduate Algebra Symposium
Organizers :  Rebekah Aduddell · Chelsea Drescher · Erin Hausmann · Naomi Krawzik · Pablo S. Ocal · Ryan Reynolds
Chair :  Nida Obatake

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Description

The Graduate Algebra Symposium is a workshop organized and run by graduate students, for graduate students. The goal of the workshop is to bring together graduate students from Universities in the area to discuss their common interests in Algebra. This is achieved by a conference style gathering where participants are encouraged to share their research with other graduate students in our field, gain experience in giving talks, and build a network of local researchers. This is a collaborative effort between Oklahoma State University, the University of Oklahoma, the University of North Texas, the University of Texas at Arlington, and Texas A&M University.

The workshop will be held on

  • Saturday October 19 in Blocker Building, room 117, from 9:00 am to 2:00 pm.

This will be the first edition of the Graduate Algebra Symposium held at Texas A&M University.

Registration and Participants

Registration is now closed. Registration was open until October 11 at 23:59 CDT through the Registration Form. Here is the list of registered participants.

Schedule
8:00-8:55Coffee and light refreshments
8:55-9:00Opening remarks
9:00-9:20Dustin McPhate (A&M): Resolutions for Truncated Ore Extensions
We begin by introducing the notions of a twisted tensor product of algebras and the class of algebras known as Ore extensions. We will then develop a method for constructing projective resolutions for modules over a certain class of twisted tensor products. We do this by first taking note of the conditions necessary to think of these algebras as a type of Ore extension and then use this parallel to extend recent results.
9:25-9:45Tolulope Oke (A&M): Derivation Operators for a Family of Quiver Algebras
Hochschild cohomology of an associative algebra has two binary operations: the cup product making it into a graded commutative ring and a graded Lie bracket making it into a Gerstenhaber algebra. We present a technique for computing the brackets of a derivation and any cocycle using any projective bi-module resolution of the algebra.
9:50-10:10Aleksandra Sobieska (A&M): Toward Free Resolutions Over Scrolls
Free resolutions over the polynomial ring have a storied and active record of study. However, resolutions over other rings are much more mysterious; even simple examples can be infinite! In these cases, we look to any combinatorics of the ring to glean information. This talk will present a minimal free resolution of the ground field over the semigroup ring arising from rational normal 2-scrolls, and (if time permits) a computation of the Betti numbers of the ground field for all rational normal k-scrolls.
10:15-10:25Break
10:25-10:45Jiajun Hoo (SHSU): Difference Sets in 2-Groups and Their Codes
Difference sets often find relevance in fields such as quantum cryptography, error correction, and signal processing. In this particular paper, we present a relation between Hadamard difference sets, bent functions, and Reed-Muller Codewords. Examination of so-called incidence matrices of difference sets admits a analytical tool with which one can generate partitions relating to coset hyperplanes of subgroups of the group with which a difference set is assocaited. The results of this paper contend with specific relations between linear combinations of rows of the incidence matrix and Reed-Muller Codewords, while assessing some properties of the ranks of both the incidence matrix and the Schur rank of said incidence matrices.
10:50-11:10John Miller (BU): Explicit Pieri Inclusions
Pieri inclusions, that is, embeddings of summands of Weyl Modules that arise via the Pieri rule, were first studied by Weyman in his thesis and first given explicitly by Olver in 1982. More recently, these maps have appeared in the work of Eisenbud, Fløstad, and Weyman and of Sam and Weyman to compute pure free resolutions for classical groups. In this talk we give a more efficient algorithm for computing these maps and describe the map in a general closed form.
11:15-11:35Naomi Krawzik (UNT): Graded Hecke Algebras in Positive Characteristic
We examine some noncommutative algebras along with their deformations. The emphasis will be on deformations of skew group algebras, which have been well studied when the characteristic of the underlying field is zero. Not so much is known when the characteristic of the field divides the order of the group acting. We present a classification of the graded Hecke algebras arising from the symmetric group acting on a polynomial ring in positive characteristic.
11:35-11:40Picture
11:40-12:40Lunch
12:40-1:00Alexander Ruys de Perez (A&M): Max Intersection Complete Codes and the Factor Complex
A place cell is a neuron corresponding to a subset of Euclidean space known as a place field, that will fire if and only if the individual to which the neuron belongs is within that place field. The firing patterns of a collection of n place fields can be represented by a neural code C on n neurons, which is a subset of 2n . Determining whether C is convex, meaning that there is an arrangement of convex place fields for which C is the code, remains an open problem. A sufficient condition for convexity is being max intersection complete: any intersection of maximal codewords is also a codeword. Currently, the only way to determine this property is to evaluate all such intersections. We present a new method to determine max intersection completeness by introducing a simplicial complex for a code C called the factor complex ∆O(C) of C. We show how to construct ∆O(C) using Stanley-Reisner theory, describe how ∆O(C) encodes information about C, and give an algorithm to check whether C is max intersection complete using the factor complex of a closely related code.
1:05-1:25Dwight A. Williams II (UTA): Super Black Magic
A Black guy shows you an infinitely large room filled with infinitely many people and tells you all of their names after shuffling them around and splitting the room into two: he claims to decompose an infinite-dimensional tensor product representation of the Lie superalgebra osp(1|2n) and provides an explicit basis of each submodule of the decomposition.
1:30-1:50Rebekah Aduddell (UTA): Support and Rank Varieties of Totally Acyclic Complexes
Originally defined for modules over a group algebra of an elementary p-group, rank and support varieties were later generalized for modules over arbitrary commutative local complete intersection rings. This talk will discuss the further generalization of support and rank varieties of modules to the triangulated category of totally acyclic complexes over a complete intersection ring, focusing on the motivation for doing so.
1:55-2:00Closing remarks
Parking

The venue is Blocker Building.

There is no free parking available on campus. The North Side Parking Garage is the closest on campus parking to the venue, only a few steps away from it. The College Main Parking Garage is the closest off campus parking to the venue, within walking distance but several minutes away from it.

The Century Square Parking Garage is open to the public, rarely charges fees, and is within walking distance from the venue, but be warned that you are parking here at your own risk.

Acknowledgements

The organizers would like to acknowledge the generous financial support of the Department of Mathematics at Texas A&M University, who also provided the venue for the event. This symposium is part of the conferences and workshops they host.

The organizers would also like to thank Kris Watkins and Qing Zhang for their logistical help.