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# Mathematical Physics

This series consists of talks in the area of Mathematical Physics.

## Seminar Series Events/Videos

Currently there are no upcoming talks in this series.

## MPIM/PI teleseminar on categorified knot invariants - 4

Vendredi mai 18, 2018
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## MPIM/PI teleseminar on categorified knot invariants - Higher structures and 4-manifolds

Vendredi mai 18, 2018
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In this talk we will discuss three (intimately related) examples of 4-manifold invariants based on higher structures:
- VOA[M4] from transgression of EFTs;
- SW and Donaldson invariants as chiral algebra correlators;
- Massey triple products from trisections.
These topics are based, respectively, on work with A.Gadde, P.Putrov (and work to appear with B.Feigin); recent paper with M.Dedushenko and P.Putrov; and a solo paper of the speaker.

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## MPIM/PI teleseminar on categorified knot invariants - Skew Howe duality and categorified knot invariants

Jeudi mai 17, 2018
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Skew Howe duality is based on a very simple observation: the set of n by m matrices has commuting action of SL_n and SL_m.  We can use this observation to study morphisms of GL_m representations using GL_n.  This perspective has proven very useful in recent years for studying quantum knot invariants and their categorifications.  I will survey work in this direction from the last 10 years, including more recent developments concerning annular skew Howe duality and annular knot invariants.

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## MPIM/PI teleseminar on categorified knot invariants - Zed-hat

Jeudi mai 17, 2018
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In this talk, intended for a broader audience, I promise to use techniques only at the level of university calculus. While staying at this level, our goal will be to learn conceptual lessons for categorification of quantum group invariants of knots and 3-manifolds, also known as the Witten-Reshetikhin-Turaev (or WRT) invariants. In particular, we will introduce new q-series invariants of 3-manifolds that have integer powers and integer coefficients and, if time permits, discuss their various constructions and properties. The talk is based on several papers with D. Pei and/or P. Putrov, C.

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## TBA

Lundi mai 14, 2018
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Abstract TBA

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## Braided tensor categories and the cobordism hypothesis

Lundi mai 07, 2018
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The cobordism hypothesis gives a functorial bijection between oriented

n-dimensional fully local topological field theories, valued in some

higher category C, and the fully dualizable object of C equipped with

the structure of SO(n)-fixed point.  In this talk I'll explain recent

works of Haugseng, Johnson-Freyd and Scheimbauer which construct a

Morita 4-category of braided tensor categories, and I'll report on joint

work with Brochier and Snyder which identifies two natural subcategories

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## TBA - Adina Gamse

Lundi mai 07, 2018

TBA

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## Construction of unitary Segal CFTs

Lundi avr 30, 2018
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In this talk I will describe joint work in progress with Andre Henriques to construct examples of Graeme Segal's functorial definition of 2d chiral conformal field theory. While Segal's definition originated in the 1980's, constructive aspects of the theory continue to be challenging, especially with regard to higher genus surfaces. I will motivate and introduce Segal's definition, and describe a new approach to constructing examples using von Neumann algebras.

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## What else can you do with solvable approximations?

Lundi mar 12, 2018
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Recently, Roland van der Veen and myself found that there are sequences of solvable Lie algebras "converging" to any given semi-simple Lie algebra (such as sl(2) or sl(3) or E8). Certain computations are much easier in solvable Lie algebras; in particular, using solvable approximations we can compute in polynomial time certain projections (originally discussed by Rozansky) of the knot invariants arising from the Chern-Simons-Witten topological quantum field theory.

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## Decomposable Specht modules

Lundi mar 05, 2018
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I will give a brief survey of the study of decomposable Specht modules for the symmetric group and its Hecke algebra, which includes results of Murphy, Dodge and Fayers, and myself. I will then report on an ongoing project with Louise Sutton, in which we are studying decomposable Specht modules for the Hecke algebra of type $B$ indexed by `bihooks’.

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## LECTURES ON-DEMAND

### Roger Melko: Perimeter Institute and University of Waterloo

Speaker: Roger Melko