## news

##### Mike Hopkins Named 2021 AMS Fellow

Mike Hopkins, George Putnam Professor of Pure and Applied Mathematics and Department Chair has been named a Fellow of the American Mathematical Society for 2021:...

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## upcoming events

< 2020 >
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• MATHEMATICAL PICTURE LANGUAGE SEMINAR

##### MATHEMATICAL PICTURE LANGUAGE SEMINARTopological order, tensor networks and subfactors

10:00 AM-11:00 AM
December 1, 2020

We present recent progress on studies of 2-dimensional topological order in terms of tensor networks and its connections to subfactor theory. We explain how Drinfel’d centers and higher relative commutants naturally appear in this context and use of picture language in this study.

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• CMSA EVENT: CMSA Math Science Literature Lecture Series

##### CMSA EVENTCMSA Math Science Literature Lecture Series

8:00 AM-9:30 AM
December 2, 2020

TITLE: Is relativity compatible with quantum theory?

ABSTRACT: We review the background, mathematical progress, and open questions in the effort to determine whether one can combine quantum mechanics, special relativity, and interaction together into one mathematical theory. This field of mathematics is known as “constructive quantum field theory.” Physicists believe that such a theory describes experimental measurements made over a 70 year period and now refined to 13-decimal-point precision—the most accurate experiments ever performed.

Talk chair: Zhengwei Liu

Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”

##### Register here to attend.
• RANDOM MATRIX SEMINAR

##### RANDOM MATRIX SEMINARJoint Dept. of Mathematics and CMSA Random Matrix & Probability Theory Seminar: Thermodynamics of a hierarchical mixture of cubes

2:00 PM-3:00 PM
December 2, 2020

The talk discusses a toy model for phase transitions in mixtures of incompressible droplets. The model consists of non-overlapping hypercubes of side-lengths 2^j, j\in \N_0. Cubes belong to an admissible set such that if two cubes overlap, then one cube is contained in the other, a picture reminiscent of Mandelbrot’s fractal percolation model. I will present exact formulas for the entropy and pressure, discuss phase transitions from a fluid phase with small cubes towards a condensed phase with a macroscopic cube, and briefly sketch some broader questions on renormalization and cluster expansions that motivate the model. Based on arXiv:1909.09546 (J. Stat. Phys. 179 (2020), 309-340).

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• CMSA EVENT: CMSA Math Science Literature Lecture Series

##### CMSA EVENTCMSA Math Science Literature Lecture Series

8:00 AM-9:30 AM
December 4, 2020

TITLE: Michael Atiyah: Geometry and Physics

ABSTRACT: In mid career, as an internationally renowned mathematician, Michael Atiyah discovered that some problems in physics responded to current work in algebraic geometry and this set him on a path to develop an active interface between mathematics and physics which was formative in the links which are so active today. The talk will focus, in a fairly basic fashion, on some examples of this interaction, which involved both applying physical ideas to solve mathematical problems and introducing mathematical ideas to physicists.

Talk chair: Peter Kronheimer

Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”

##### Register here to attend.
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• NUMBER THEORY SEMINAR

##### NUMBER THEORY SEMINARHermite interpolation and counting number fields

3:00 PM-4:00 PM
December 9, 2020

There are several ways to specify a number field. One can provide the minimal polynomial of a primitive element, the multiplication table of a $\bf Q$-basis, the traces of a large enough family of elements, etc. From any way of specifying a number field one can hope to deduce a bound on the number $N_n(H)$ of number fields of given degree $n$ and discriminant bounded by $H$. Experimental data suggest that the number of isomorphism classes of number fields of degree $n$ and discriminant bounded by $H$ is equivalent to $c(n)H$ when $n\geqslant 2$ is fixed and $H$ tends to infinity. Such an estimate has been proved for $n=3$ by Davenport and Heilbronn and for $n=4$, $5$ by Bhargava. For an arbitrary $n$ Schmidt proved a bound of the form $c(n)H^{(n+2)/4}$ using Minkowski’s theorem. Ellenberg et Venkatesh have proved that the exponent of $H$ in $N_n(H)$ is less than sub-exponential in $\log (n)$. I will explain how Hermite interpolation (a theorem of Alexander and Hirschowitz) and geometry of numbers combine to produce short models for number fields and sharper bounds for $N_n(H)$.

Password: The order of the permutation group on 9 elements.

• CMSA EVENT: CMSA New Technologies in Mathematics: Machine learning and SU(3) structures on six manifolds

##### CMSA EVENTCMSA New Technologies in Mathematics: Machine learning and SU(3) structures on six manifolds

3:00 PM-4:00 PM
December 9, 2020

In this talk we will discuss the application of Machine Learning techniques to obtain numerical approximations to various metrics of SU(3) structure on six manifolds. More precisely, we will be interested in SU(3) structures whose torsion classes make them suitable backgrounds for various string compactifications. A variety of aspects of this topic will be covered. These will include learning moduli dependent Ricci-Flat metrics on Calabi-Yau threefolds and obtaining numerical approximations to torsional SU(3) structures.

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