Mathematics Home / Research Seminars: Algebra and Combinatorics
Time & Location: All talks are on Wednesday in Gibson Hall 127 at 3:00 PM unless otherwise noted.
Organizer: Mahir Can
Title: Decomposable Specht modules
Liron Speyer | Okinawa Institute of Science and Technology
Abstract:
I will give a brief survey of the study of decomposable Specht modules for the symmetric group and its Hecke algebra, which includes results of Murphy, Dodge and Fayers, and myself, before reporting on recent work with Louise Sutton, in which we have studied decomposable Specht modules for the Hecke algebra of type $B$ indexed by `bihooks’. I will present our conjectured classification of decomposable Specht modules indexed by bihooks, which we proved `one half of’, and some ongoing work in explicitly determining the structure of those decomposable Specht modules.
Location: Gibson Hall 127
Time: 3:00
Title: Gorenstein polytopes
Takayuki Hibi | Osaka University
Abstract:
A Gorenstein polytope is a lattice polytope one of whose dilated polytopes is a reflexive polytope. In my talk, after reviewing Gorenstein polytopes from a viewpoint of enumeration of lattice points, several conjectures arising from Gorenstein polytopes will be reported. No special knowledge will be required to understand my talk.
Title: Total nonnegativity and induced sign characters of the Hecke algebra
Mark Skandera | Lehigh University
Abstract:
Gantmacher's study of totally nonnegative (TNN) matrices in the 1930's eventually found applications in many areas of mathematics. Descending from his work are problems concerning TNN polynomials, those polynomial functions of n^2 variables which take nonnegative values on TNN matrices. Closely related to TNN polynomials are functions in the Hecke algebra trace space whose evaluations at certain Hecke algebra elements yield polynomials in N[q]. In all cases, it would be desirable to combinatorially interpret the resulting nonnegative numbers. In 2017, Kaliszewski, Lambright, and the presenter found the first cancellation-free combinatorial formula for the evaluation of all elements of a basis of V at all elements of a basis of the Hecke algebra. We will discuss a recent improvement upon this result which also advances our understanding of TNN polynomials. This is joint work with Adam Clearwater.
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Title: Symbolic powers and the (stable) containment problem
Eloísa Grifo | University of California at Riverside
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The n-th power of an ideal is easy to compute, though difficult to describe geometrically. In contrast, symbolic powers of ideals, which arise naturally from the theory of primary decomposition, are difficult to compute but have a natural geometric description.
In trying to compare symbolic and ordinary powers, Harbourne conjectured that a famous containment by Ein--Lazersfeld--Smith, Hochster--Huneke, and Ma--Schwede could be improved. Harbourne's Conjecture is a statement depending on n that has been disproved for particular values of n. However, recent evidence points towards a stable version of Harbourne's conjecture, where we substitute all n by all n large enough. Some of that evidence is joint work with Craig Huneke and Vivek Mukundan.
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Title: Classical Mechanics, Symplectic Geometry, Combinatorics
Tewodros Amdeberhan | Tulane University
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In this semi-expository talk, we give a brief on classical mechanics in the Hamiltonian setting, describe it in the symplectic framework and draw out some interesting combinatorics. The discussion will be accessible to all.
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