This Week in Mathematics


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Entries for this week: 5

Tuesday April 23, 2024

Topology and Geometry Seminar [url]
Symmetry properties of the cubical Joyal model structure
- Brandon Doherty, FSU
Time: 3:05 Room: LOV 107
Abstract/Desc: Via the cubical Joyal model structure, cubical sets having faces, degeneracies and connections can be viewed as models for (infinity,1)-categories; in this model, homotopies are most naturally defined using the geometric product, rather than the cartesian product. This is an alternative monoidal product having convenient properties, but with the drawback that it is not symmetric. In this talk, based on work in progress joint with Tim Campion, we discuss a comparison between the less structured cubical sets on which the cubical Joyal model structure is defined and cubical sets with symmetries, which allows us to prove that the geometric product is symmetric up to natural weak equivalence in the cubical Joyal model structure. If time permits, we will also discuss applications of this comparison to the construction of a Quillen-equivalent model structure on symmetric cubical sets, and the potential application of similar techniques to proving that the cubical Joyal model structure is monoidal with respect to the cartesian product.

Wednesday April 24, 2024

Applied and Computational Math Seminar -- Stochastic Computing and Optimization
Stochastic Computing and Optimization
- ACM/Fin Math students,
Time: 3:05PM Room: LOV 0231
Abstract/Desc: Students from ACM and Financial Math will present their research progress. Some invited speakers may also present their research.

Biomathematics Seminar
The impact of zealots and consensus makers in voting games
- Jonathan Engle, FSU
Time: 3:05 Room: LOV 232
Abstract/Desc: The outcome of democratic elections rests on individuals' decision-making that is driven by their varying preferences and sets of information. Individuals may prefer consensus to deadlock, or deadlock to consensus, and information may be fractured via echo-chambers. To understand the role of these factors in elections reaching consensus, we explore a voter game in which two parties are composed of zealots, who always vote for their party, consensus makers, who vote for the party who previously won, and strategists, who base their vote on their prediction of which party will win. Voters may change their voting strategy either by imitating others or reconsidering their strategy based on their respective payoffs. We consider various preference orderings of one's own party winning, the opposing party winning, and deadlock, and we also consider different information networks where knowledge of the voting behaviour of others is incomplete and heterogeneous. We show that zealots and consensus-makers dominate over long time if the rate of imitation of others is low and consensus can frequently be reached. When this is not the case, zealots dominate and thus deadlock is unavoidable. Furthermore, we show that consensus is promoted by an uneven distribution of party membership, and undermined when it is even. Strategists also undermine consensus regardless of preference to gridlock over party alignment.

Biomathematics Journals
A Multiscale Model of Complex Endothelial Cell Dynamics in Early Angiogenesis
- James Thornham, FSU
Time: 5:00 Room: 216 Dirac Library

Friday April 26, 2024

Mathematics Colloquium
Random Fractals Arising in Probability and Statistical Physics
- Greg Lawler, University of Chicago
Time: 3:05 Room: Lov 101
Abstract/Desc: Many of the mathematical structures arising in statistical physics viewed at phase transitions are fractals that are random but have some kinds of “statistical self-similarity’’. One prototypical model is the “self-avoiding walk”, a path of a walker who moves ``randomly’’ except with the restriction that no place is revisited. The last twenty-five years have seen significant advances in the mathematical understanding of these fractals. I will introduce some of these focusing primarily on planar models which have been the focus of most of the successes. This talk is designed for a general mathematical audience and does not assume background in probability or statistical physics.

Problems? Email webmaster@math.fsu.edu.

Department of Mathematics

This Week in Mathematics