Seminar Calendar
for Algebra, Geometry and Combinatorics events the next 12 months of Sunday, January 1, 2017.

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events for the
events containing

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 19, 2017

Algebra, Geometry and Combinatorics
3:00 pm   in 347 Altgeld Hall,  Thursday, January 19, 2017
 Del Edit Copy
Submitted by lescobar.
 Balazs Elek (Cornell University)Pizzas and Toric surfaces with Kazhdan-Lusztig atlasesAbstract: A Bruhat atlas, introduced by He, Knutson and Lu, on a stratified variety is a way of modeling the stratification locally on the stratification of Schubert cells by opposite Schubert varieties. They described Bruhat atlases on many interesting varieties, including partial flag varieties and on wonderful compactifications of groups. We will discuss some results toward a classification of varieties with Bruhat atlases, focusing on the 2-dimensional toric case. In this case, the answer may be stated in terms of the moment polygon of the toric surface, which one should first slice up, then put toppings on, much like one would do while preparing a pizza.

Thursday, February 16, 2017

Algebra, Geometry and Combinatorics Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, February 16, 2017
 Del Edit Copy
Submitted by lescobar.
 Cara Monical (UIUC)Set-Valued SkylinesAbstract: Set-valued tableaux play an important role in combinatorial $K$-theory. Separately, semistandard skyline fillings are a combinatorial model for Demazure atoms and key polynomials. We unify these two concepts by defining a set-valued extension of semistandard skyline fillings and then give analogues of results of J. Haglund, K. Luoto, S. Mason, and S. van Willigenberg.

Thursday, February 23, 2017

Algebra, Geometry and Combinatorics Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, February 23, 2017
 Del Edit Copy
Submitted by lescobar.
 Bennet Goeckner (The University of Kansas)A non-partitionable Cohen-Macaulay complexAbstract: Stanley conjectured in 1979 that all Cohen-Macaulay complexes were partitionable. We will construct an explicit counterexample to this conjecture, which also disproves a related conjecture about the Stanley depth of monomial ideals. This talk is based on joint work with Art Duval, Caroline Klivans, and Jeremy Martin. No prerequisite knowledge of simplicial complexes or commutative algebra will be assumed.

Friday, March 3, 2017

Algebra, Geometry and Combinatorics Seminar
1:00 pm   in 347 Altgeld Hall,  Friday, March 3, 2017
 Del Edit Copy
Submitted by lescobar.
 Bernd Schober (University of Toronto)Embedded resolution of singularities in dimension twoAbstract: When studying a singular variety one aims to find a variety that shares many properties with the original one, but that is easier to handle. One way to obtain this is via resolution of singularities. In contrast to the quite well understood situation over fields of characteristic zero, only little is known in positive or mixed characteristic and resolution of singularities remains still an important open problem. One of the key ideas over fields of characteristic zero is the notion of maximal contact. After briefly explaining its power, I will point out problems that arise in positive characteristic. Then I will focus on the known two-dimensional case and will discuss the resolution algorithm constructed by Cossart, Jannsen and Saito. Finally, I will explain how polyhedra can be used to detect the improvement of the singularity along the process. This is joint work with Vincent Cossart.

Thursday, March 9, 2017

Algebra, Geometry and Combinatorics Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, March 9, 2017
 Del Edit Copy
Submitted by lescobar.
 Yan Zhang (San Jose State University)A Combinatorial approach to SupersymmetryAbstract: Adinkras are combinatorial tools created to study representations in supersymmetry. Besides having inherent interest for physicists, adinkras offer many easy-to-state and accessible open problems for mathematicians from many diverse subfields including Clifford algebras, posets, coding theory, and algebraic topology. I will discuss some results and problems, but mostly focusing on sharing some very pretty combinatorial objects with you.

Thursday, March 16, 2017

Algebra, Geometry and Combinatorics Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, March 16, 2017
 Del Edit Copy
Submitted by lescobar.
 Reuven Hodges (Northeastern University)Levi subgroup actions on Schubert varieties in the GrassmannianAbstract: Let L be the Levi part of the stabilizer in GL_N(C) (for left multiplication) of a Schubert variety X(w) in the Grassmannian. For the induced action of L on C[X(w)], the homogeneous coordinate ring of X(w) (for the Plucker embedding), I will give a combinatorial description of the decomposition of C[X(w)] into irreducible L-modules. Using this combinatorial description, I give a classification of all Schubert varieties X(w) in the Grassmannian for which C[X(w)] has a decomposition into irreducible L-modules that is multiplicity free. This classification is then used to show that certain classes of Schubert varieties are spherical L-varieties. Also, I will describe interesting related results on the singular locus of X(w) and multiplicities at points in X(w).

Thursday, March 30, 2017

Algebra, Geometry and Combinatorics Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, March 30, 2017
 Del Edit Copy
Submitted by lescobar.
 Steven Karp (UIUC)The m=1 amplituhedron and cyclic hyperplane arrangementsAbstract: The m=1 amplituhedron and cyclic hyperplane arrangements The totally nonnegative part of the Grassmannian Gr(k,n) is the set of k-dimensional subspaces of R^n whose Plücker coordinates are all nonnegative. The amplituhedron is the image in Gr(k,k+m) of the totally nonnegative part of Gr(k,n), through a (k+m) x n matrix with positive maximal minors. It was introduced in 2013 by Arkani-Hamed and Trnka in their study of scattering amplitudes in N=4 supersymmetric Yang-Mills theory. Taking an orthogonal point of view, we give a description of the amplituhedron in terms of sign variation. We then use this perspective to study the case m=1, giving a cell decomposition of the m=1 amplituhedron and showing that we can identify it with the complex of bounded faces of a cyclic hyperplane arrangement. It follows that the m=1 amplituhedron is homeomorphic to a ball. This is joint work with Lauren Williams.

Thursday, April 13, 2017

Algebra, Geometry and Combinatorics Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, April 13, 2017
 Del Edit Copy
Submitted by lescobar.
 Maria Gillespie (UC Davis)A crystal structure on shifted tableaux, with applications to type B Schubert curvesAbstract: We present a new crystal-like structure on shifted (marked) semistandard skew tableaux. The raising and lowering operators commute with jeu de taquin slides, and detect the type B Littlewood-Richardson condition as the highest weight entries. Certain substructures satisfy the Kashiwara crystal axioms for the root system of $\mathrm{GL}_n$. If time permits, we will discuss applications of our new operators to Schubert curves in the orthogonal Grassmannian. This is joint work with Jake Levinson and Kevin Purbhoo.