Department of

Mathematics


Seminar Calendar
for Commutative Ring Theory events the next 12 months of Sunday, January 1, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2016           January 2017          February 2017    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
              1  2  3    1  2  3  4  5  6  7             1  2  3  4
  4  5  6  7  8  9 10    8  9 10 11 12 13 14    5  6  7  8  9 10 11
 11 12 13 14 15 16 17   15 16 17 18 19 20 21   12 13 14 15 16 17 18
 18 19 20 21 22 23 24   22 23 24 25 26 27 28   19 20 21 22 23 24 25
 25 26 27 28 29 30 31   29 30 31               26 27 28            
                                                                   

Thursday, January 26, 2017

3:00 pm in 243 Altgeld Hall,Thursday, January 26, 2017

Organizational Meeting

Thursday, March 2, 2017

3:00 pm in 243 Altgeld Hall,Thursday, March 2, 2017

Multidimensional Persistent Homology

Hal Schenck (UIUC Math)

Abstract: A fundamental tool in topological data analysis is persistent homology, which allows detection and analysis of underlying structure in large datasets. Persistent homology (PH) assigns a module over a principal ideal domain to a filtered simplicial complex. While the theory of persistent homology for filtrations associated to a single parameter is well-understood, the situation for multifiltrations is more delicate; Carlsson-Zomorodian introduced multidimensional persistent homology (MPH) for multifiltered complexes via multigraded modules over a polynomial ring. We use tools of commutative and homological algebra to analyze MPH, proving that the MPH modules are supported on coordinate subspace arrangements, and that restricting an MPH module to the diagonal subspace $V(x_i-x_j | i \ne j)$ yields a PH module whose rank is equal to the rank of the original MPH module. This gives one answer to a question asked by Carlsson-Zomorodian. This is joint work with Nina Otter, Heather Harrington, Ulrike Tillman (Oxford).

Thursday, October 19, 2017

3:00 pm in 243 Altgeld Hall,Thursday, October 19, 2017

Koszul almost complete intersections

Matthew Mastroeni (UIUC Math)

Abstract: Let $R = S/I$ be a quotient of a standard graded polynomial ring $S$ by an ideal $I$ generated by quadrics. If $R$ is Koszul, a question of Avramov, Conca, and Iyengar asks whether the Betti numbers of $R$ over $S$ can be bounded above by binomial coefficients on the minimal number of generators of $I$. Motivated by previous results for Koszul algebras defined by three quadrics, we give a complete classification of the structure of Koszul almost complete intersections and, in the process, give an affirmative answer to the above question for all such rings.