[geometry-ml:03207] MS seminar at Kavli IPMU -- Anton Khoroshkin and Yefeng Shen -- Jan 9, 2018

[Todor Milanov]

Dear all,

I would like to announce the following two Mathematics and String theory seminars at Kavli IPMU. 

1) Speaker: Anton Khoroshkin (HSE Moscow)
Date: Tue, Jan 09, 2018, 13:15 - 14:45
Place:	Seminar Room A

Title: Cacti groups, an operadic point of view

Abstract: The category of representations over a quantum group $U_q(g)$ form a braided tensor category that produces an action of the (pure) braid groups on tensor products. Respectively, the category of crystals (which is a limit for q tends to zero) form a coboundary category together with an action of (pure) cacti group on tensor products. 

The little discs operad is an operad whose space of $n$-ary operations is the Eilenberg-Maclane space of the pure braid groups with $n$ braids.
Correspondingly, the real loci of the moduli spaces of stable rational curves with marked points assemble an operad of the Eilenberg-Maclane spaces of pure cacti groups. 

I will present the detailed description of the latter operad as well as its deformation theory and relationships with the little discs operad. Among different applications I will prove rational K(\pi,1) property of the latter moduli spaces as well as other interesting properties of the pure cacti groups that were conjectured by P.Etingof, A.Henriques, J.Kamnitzer and E.Rains in the seminal paper arXiv:math/0507514.
 Talk is based on the joint work with Thomas Willwacher.

2) Speaker: Yefeng Shen	(U of Oregon)
Date:	Tue, Jan 09, 2018, 15:30 - 17:00
Place:	Seminar Room B

Title:	Landau-Ginzburg/Calabi-Yau correspondence in one dimension	 more

Abstract: One way to understand Landau-Ginzburg/Calabi-Yau 
correspondence is to study Gromov-Witten theory of a Calabi-Yau variety 
(or orbifold) and Fan-Jarvis-Ruan-Witten theory of a counterpart LG 
model for a quasi homogeneous polynomial. When the target Calabi-Yau is 
one dimensional, their GW/FJRW invariants are controlled by tautological 
relations and WDVV equations. They are coefficients of expansions of 
appropriate quasi-modular forms at different points. As a consequence, 
we can relate these expansions by Cayley transformations. We will also 
compare this method with Milanov-Ruan's realization of LG/CY 
correspondence in orbifold cases.


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Todor Eliseev Milanov
Associate Professor 
Kavli IPMU,  Japan

todor.milanov ＠ ipmu.jp