Title: My preferred proof of the Lefschetz fixed point theorem 

Abstract: There are many different proofs of the Lefschetz fixed point theorem.  The most familiar approach uses simplicial approximation and is often a first example of the power of simplicial homology.  I'll talk about a very different proof that I find much more useful.  This proof requires more input, but it generalizes easily. 

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Dr. Chang-Guo Zhan will be presenting a seminar titled Drug Discovery and Development via Computational Design.  

Faculty Host: Dr. Dong-Sheng Yang

Informal lunch with Martina Bode, Charles Deering McCormick University Distinguished Lecturer at Northwestern University. This is part of our teaching workshop on Clickers in the Mathematics Classroom.

This event is part of a teaching workshop sponsored by the College of Arts and Sciences

Lingfeng Tang

Biology Department

Mentor: Dr. Doug Harrison

Title:  The polytope of Tesler matrices

Abstract:  Tesler matrices are upper triangular matrices with nonnegative integer entries with certain restrictions on the sums of their rows and columns. Glenn Tesler studied these matrices in the 1990s and in 2011 Jim Haglund rediscovered them in his study of diagonal harmonics. We investigate a polytope whose integer points are the Tesler matrices. It turns out that this polytope is a flow polytope of the complete graph thus relating its lattice points to vector partition functions. We study the face structure of this polytope and show that it is a simple polytope. We show its h-vector is given by Mahonian numbers and its volume is a product of consecutive Catalan numbers and the number of Young tableaux of staircase shape.  This is joint work with Brendon Rhoades and Karola Mészàros.

Title:  Algebraic models in systems biology

Abstract:  Progress in systems biology relies on the use of mathematical and statistical models for system level studies of biological processes. Several different modeling frameworks have been used successfully, including traditional differential equations based models, a variety of stochastic models, agent-based models, and Boolean networks, to name some common ones. This talk will focus on discrete models and the challenges they present, in particular model stability and data selection.

All are welcome to come and mingle over coffee, tea, and cookies

Title:  The Freudenthal Suspension Theorem

Abstract:  The Freudenthal suspension theorem asserts that for an (n-1)-connected CW complex X the suspension map from \pi_i(X) to \pi_{i+1}(SX) is an isomorphism for i < 2n - 1 and a surjection for i = 2n - 1. We will introduce relative homotopy groups and the long exact sequence in homotopy groups for a space X and a subspace A. With these tools we will show how the Freudenthal suspension theorem follows from the homotopy excision theorem. Time permitting, we will examine some consequences for homotopy groups of spheres.

Topic:  Hubs and Authorities

Abstract:  We introduce the idea of Hub and Authority rankings inside large scale networks with appropriate historical context, and introduce a new form for calculating Hubs and Authorities by turning a directed network into a bipartite network, along with efficient computational tools to evaluate these rankings in large scale networks.