Multiplicities is a broad audience seminar geared towards transversal topics whose aim is to highlight the diversity of mathematics and mathematicians.

It is especially intended for PhD students, interested in widening their horizons and is supported by the PRIDE Grant “Geometry, Probability and their Synergies (GPS)”.


 April 2, 2019

Béatrice de Tilière, The Z-invariant Ising model via dimers

 June 18, 2019

Diana Davis, Periodic paths on the pentagon

 May 12, 2020

Olga Paris-Romaskevich, Triangle tiling billiards, interval exchange transformations with flips and movies

 Mars 23, 2021

Persi Diaconis, Adding numbers and shuffling cards

 May 11, 2021

Allison Henrich, Knotty Games

 June 15, 2021

Lisa Sauermann, T.B.A.

Béatrice de Tilière

The Z-invariant Ising model via dimers

 April 1, 2019    16:00 - 16:50
 MNO 1.020, Campus Belval

Abstract. The Ising model is one of the most classical models of statistical mechanics. We shall present its relation to dimers, its Z-invariant version and some results obtained with C. Boutillier and K. Raschel.

Diana Davis

Periodic paths on the pentagon

 June 18, 2019    16:30 - 17:20
 MNO 1.020, Campus Belval

Abstract. Mathematicians have long understood periodic trajectories on the square billiard table, which occur when the slope of the trajectory is rational. In this talk, I'll explain my joint work with Samuel Lelièvre on periodic trajectories on the regular pentagon, describing their geometry, symbolic dynamics, and group structure. The periodic trajectories are very beautiful, and some of them exhibit a surprising "dense but not equidistributed" behavior.

Olga Paris-Romaskevich

Triangle tiling billiards, interval exchange transformations with flips and movies

 May 12, 2020  Postponed
 MNO 1.020, Campus Belval

Abstract. T.B.A.

Persi Diaconis

Adding numbers and shuffling cards

 March 23, 2021    16:00 - 16:50
 Zoom meeting

Abstract. When numbers are added in the usual way, ``carries'' appear along the way. If you are me (and hopefully you after this talk) it's natural to ask: ``How do the carries go? How many are there and, if you just had a carry, is it more or less likely that the next sum has a carry?'' Strangely, carries form a Markov chain with an ``amazing'' transition matrix. More strangely, this same matrix appears in the analysis of the usual way of riffle shuffling cards. I will explain the connection, tell you about the ``seven shuffles theorem'' and attempt to do it ``in English''.

Alison Henrich

Knotty Games

 May 11, 2021    16:00 - 16:50
 Zoom meeting

Abstract. Far too many people in this world are under the mistaken impression that math can't be fun. The aim of much of my research with student and faculty collaborators, in part, is to provide yet another counterexample to this claim. Our work combines a delightfully visual mathematical subject, knot theory, with one of the most common sources of fun: games. Motivated by the fascinating work of Ayaka Shimizu on an unknotting operation called the region crossing change and research of Ryo Hanaki on unusual types of knot diagrams called pseudodiagrams, we have invented and explored several knot games. In this talk, we will play these games on knot diagrams, developing both our spatial intuition and our understanding of the structure of knots along the way.

Lisa Sauermann


 June 15, 2021    16:00 - 16:50
 Zoom meeting

Abstract. T.B.A.