The meeting will facilitate interactions between students and faculty---with interests in ring theory, broadly interpreted---from institutions in the Southwest. It takes place at New Mexico State University in Las Cruces in the first weekend of March 2011. Six speakers will deliver hour long talks on topics within their specialty. Five speakers will be local to the Southwest region, and one will be a prominent algebraist from outside the region. The lectures will be accessible to graduate students. The meeting also features three hour-long poster sessions in which the participating students will present their research.
The study of rings, in the broadest sense, is crucial to many branches of mathematics---commutative and non-commutative geometry, group representations, number theory, coding theory, and cryptography to name a few---and touches on even more---combinatorics, homotopy theory, and statistics, for example. Algebraists in the Southwest region pursue research on a variety of topics under the umbrella of pure and applied ring theory. The geographical distances in the region are such that interactions between people at different institutions rarely happen spontaneously. The meeting will bring together students and faculty from a variety of institutions for inspiring talks and ample time for scientific interaction. One can expect that new collaborations and discoveries may result from such a meeting. About 50 participants are expected: students, young and senior faculty from New Mexico, Oklahoma, Texas, and neighboring states. Participation of students from underrepresented minority groups, women, untenured faculty, and faculty at non-Ph.D. granting institutions is particularly encouraged.
The project consisted of a two-day meeting of algebraists at New Mexico State University in Las Cruces. This was the second Southwest Local Algebra Meeting (SLAM); the first took place at the University of Texas at Arlington in March 2010. The purpose of the meeting was to facilitate interactions between students and faculty— with interests in ring theory, broadly interpreted—from institutions in the Southwest. The meeting took place in the first weekend of March 2011. Six speakers delivered 50 minute talks on topics within their specialty. Five speakers were local, from the Southwest region. These included Scott Chapman (Sam Houston State University), Dimitar Grantcharov (University of Texas at Arlington), Mara Neusel (Texas Tech University), Clarence Wilkerson (Texas A & M University), and Janet Vassilev (University of New Mexico). There was also a prominent algebraist from outside the region, namely Roger Wiegand (University of Nebraska-Lincoln). The speakers were instructed to ensure that their lectures are accessible to graduate students, and the instructions were quite faithfully followed. The meeting also featured three hour-long poster sessions in which most of the participating students presented their research. There were 19 poster in total. They were Kristen Beck (University of Texas-Arlington, "Asymmetric linear complete resolutions over short local rings"), Angela Brown (University of Texas-Arlington, "New results in finite geometries and how to connect them to K-12 mathematics"), Linlin Chen (University of Texas-Arlington, "New examples of fractional dimension of translation planes"), Nickolas Hein (Texas A&M University, "Degenerations that commute"), Daniel Hernandez (University of Michigan, "Singularities of hypersurfaces via integration and the Frobenius morphism"), Imad Jaradat (New Mexico State University, "Ga-action in C4") Youngsu Kim, (Purdue University, "When is an associated graded ring Cohen-Macaulay if it is a domain?"), Micah Leamer (University of Nebraska-Lincoln, "Asymptotic behavior of the dimensions of syzygy modules"), Paolo Mantero (Purdue University, "Cohen-Macaulayness of the square of an ideal"), Abraham Martin del Campo (Texas A&M University, "Finiteness on homogenous Markov chain models"), Zachary McGregor-Dorsey (University of Colorado-Boulder, "Full heaps over Dynkin diagrams of affine type A"), Manizheh Nafari (University of Texas-Arlington, "Constructing quadratic quantum P2 from graded skew clifford algebra"), Lan Nguyen (Purdue University, "The equations of Rees algebras of ideals with linear presentations"), Augustine O'Keefe (Tulane University, "Depth of toric rings arising from finite graphs"), Jared Painter (University of Texas-Arlington, "Trivariate monomial resolutions generic vs. non-generic"), Milos Savic (New Mexico State University, "Where is the logic in homology proofs?"), Piyush Shroff (Texas A&M University, "Cohomology of quotients of quantum symmetric algberas"), Branden Stone (University of Kansas, "Countable Cohen-Macaulay type and isolated singularities"), Emily Witt (University of Michigan, "An example of computing local cohomology"). There was also a very successful conference dinner which facilitated many further interactions between students and faculty. There were in total 65 participants: students, young and senior faculty from New Mexico, Oklahoma, Texas, and neighboring states. Participation of students from underrepresented minority groups, women, untenured faculty, and faculty at non-Ph.D. granting institutions were also present in significant numbers. Most of the NSF support was used for travel and lodging for students and faculty with limited access to travel funds. Intellectual Merit. The study of rings, in the broadest sense, is crucial to many branches of mathematics—commutative and non-commutative geometry, group representations,number theory, coding theory, and cryptography to name a few—and touches on even more—combinatorics, homotopy theory, and statistics, for example. Algebraists in the Southwest region pursue research on a variety of topics under the umbrella of pure and applied ring theory. The geographical distances in the region are such that interactions between people at different institutions rarely happen spontaneously. The meeting brought together students and faculty from a variety of institutions for inspiring talks and ample time for scientific interaction. One can expect that new collaborations and discoveries resulted from the meeting. Broader Impact. The Southwest region is home to several non-Ph.D. granting institutions. Faculty at these institutions have limited travel funds. The relative proximity of the meeting venue and the availability of participant support offered them an opportunity to connect or reconnect with research groups in their geographical region. For students who have yet to attend their first scientific meeting, this one served as a smooth introduction to the professional circles. The modest size of the meeting helped create a relaxed atmosphere, and presentations in the poster sessions helped the graduate students break the ice and interact with faculty members from other institutions. As an outcome of such interactions, one can expect that some students landed their first invitations to speak at departmental seminars or other professional meetings.
