Mathematics Dept.
  Events
University of Washington
Tue 17 Sep 2019, 4:00pm
Discrete Math Seminar
ESB 4127
Resolving Stanley’s conjecture on k-fold acyclic complexes
ESB 4127
Tue 17 Sep 2019, 4:00pm-5:00pm

Abstract

In 1993, Stanley showed that if a simplicial complex is acyclic over some field, then its face poset can be decomposed into disjoint rank 1 boolean intervals whose minimal faces together form a subcomplex. Stanley further conjectured that complexes with a higher notion of acyclicity could be decomposed in a similar way using boolean intervals of higher rank. We provide an explicit counterexample to this conjecture. We also prove a special case of the conjecture, and show that a weaker decomposition into boolean trees always exists. This is joint work with Joseph Doolittle.
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UBC
Tue 24 Sep 2019, 4:00pm
Discrete Math Seminar
ESB 4127
Normal lattice supercharacter theories and Hopf structures
ESB 4127
Tue 24 Sep 2019, 4:00pm-5:00pm

Abstract

The concept of Hopf algebras originated from the theory of algebraic groups and algebraic topology in the mid 20th century. Hopf structures have numerous applications in many other mathematical branches, and now it is a familiar concept in representation theory as the class functions and superclass functions of some tower of groups have Hopf structures. In these Hopf structures, representation theoretic functors give the product and coproduct. In this talk, we give a brief introduction to normal lattice supercharacter theories, and then we construct a Hopf structure by using these supercharacter theories.
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Nick Olson-Harris
U. Waterloo
Tue 1 Oct 2019, 4:00pm
Discrete Math Seminar
ESB 4127
TBA
ESB 4127
Tue 1 Oct 2019, 4:00pm-5:00pm

Abstract


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Chris Ryan
Sauder, UBC
Tue 8 Oct 2019, 4:00pm
Discrete Math Seminar
ESB 4127
The discrete moment problem with nonconvex shape constraints
ESB 4127
Tue 8 Oct 2019, 4:00pm-5:00pm

Abstract

The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with additional “shape constraints” that guarantee the worst-case distribution is either log-concave (LC), has an increasing failure rate (IFR), or an increasing generalized failure rate (IGFR). These classes of shape constraints have not previously been studied in the literature, in part due to their inherent nonconvexities. Nonetheless, these classes of distributions are useful in practice with applications in revenue management, reliability, and inventory control. We characterize the structure of optimal extreme point distributions. We show, for example, that an optimal extreme point solution to a moment problem with m moments and LC shape constraints is piecewise geometric with at most m pieces. 

This is joint work with Xi Chen (NYU, Stern School of Business), Simai He (Shanghai University of Finance and Economics, School of Information Management and Engineering), Bo Jiang (Shanghai University of Finance and Economics, School of Information Management and Engineering), and Teng Zhang (Stanford, Management Science and Engineering).
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UBC
Tue 22 Oct 2019, 4:00pm
Discrete Math Seminar
ESB 4127
Graph information ratio
ESB 4127
Tue 22 Oct 2019, 4:00pm-5:00pm

Abstract

Inspired by a problem in joint source-channel coding, we introduce a new notion of similarity between graphs, termed graph information ratio. We discuss various properties of this measure, including in particular metric structure and partial ordering of graphs, an information ratio power inequality, relations to graph homomorphism, algebraic identities and inequalities, and more.
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Brian Chan
UBC
Tue 29 Oct 2019, 4:00pm
Discrete Math Seminar
ESB 4127
TBA
ESB 4127
Tue 29 Oct 2019, 4:00pm-5:00pm

Abstract

 
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University of Queensland
Tue 14 Jan 2020, 4:00pm
Discrete Math Seminar
ESB 4127
ESB 4127
Tue 14 Jan 2020, 4:00pm-5:00pm

Abstract


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