Coordinator: Brendon Rhoades
Email: bprhoades (at) math.ucsd.edu
Office: 7250 APM
Colloquium Location: B402A APM
Colloquium Time: Mondays, 10:00-10:50 am

Description: This is a weekly colloquium meant to give students a fun introduction to ideas in research mathematics.

Grading: You are required to attend each colloquium. You may miss at most one colloquium to receive credit.

Schedule

1/9/2023: Brendon Rhoades
Title: Shoving boxes into corners
Abstract: A *partition* is a way to shove a finite collection of square boxes into a corner. We will explain some combinatorial, algebraic, and geometric applications of box shoving.

1/16/2023: MLK Day
Title: No colloquium

1/23/2023: Chris O'Neill (SDSU)
Title: Block designs and geometry
Abstract: In this expository talk, we explore combinatorial design theory, and discover some surprisingly deep connections along the way.

1/30/2023: Lutz Warnke
Title: Probabilistic Method in Combinatorics
Abstract: The Probabilistic Method is a powerful tool for tackling many problems in discrete mathematics and related areas. Roughly speaking, its basic idea can be described as follows. In order to prove existence of a combinatorial structure with certain properties, we construct an appropriate probability space, and show that a randomly chosen element of this space has the desired property with positive probability. In this talk we shall give a gentle introduction to the Probabilistic Method, with an emphasis on examples.

2/6/2023: Jonathan Novak
Title: Linear Algebra When Things Get Big and Random
Abstract: TBA

2/13/2023: David Meyer
Title: Hearts and Roses
Abstract: TBA

2/20/2023: President's Day
Title: No colloquium

2/27/2023: TBA
Title: TBA
Abstract: TBA

3/6/2023: Aranya Lahiri
Title: Mathematics of Morphogenesis: A seriously incomplete view
Abstract: Problems of formation and detection of shapes and forms can be traced a long way back in history. What constitutes a form, how can we distinguish between patterns of a zebra and ferromagnetic fluids, why do we always hear "nature loves Fibonacci Numbers", can self-organizing and self-reproducing sand dunes be considered alive? We can ask a wide array of simple questions that becomes extremely difficult to answer immediately. People from varied disciplines and across many centuries have spent considerable time with these questions. We can trace an incomplete network of concepts created to tackle them in the works of Goethe, D'arcy Thompson, Alan Turing, Rene Thom,etc. This thread continues in modern times, see (https://arxiv.org/abs/2101.02652) for example. My hope is to indicate how mathematicians engaged with these problems and look at concrete examples to give a sense of mathematical contributions to these questions and what new problems are created due to these necessarily partial and cautious engagements.

3/13/2023: Reuven Hodges
Title: Approximate counting in algebraic combinatorics
Abstract: I will present a general framework, building on the work of Jerrum-Valiant-Vazirani, for converting polynomial-time randomized sampling algorithms into polynomial-time approximate counting algorithms. As a specific example, we introduce a randomized algorithm for generating standard set-valued tableaux by extending the Green-Nijenhuis-Wilf hook walk algorithm. This is then used to construct a fully polynomial randomized approximation scheme for counting the number of standard set-valued tableaux.