Author: MasterLibedinsky

This author has written 45 articles
For Mathematicians / Research interests

Research interests

Most of my work revolves around some beautiful and central objects in representation theory called Soergel bimodules. I have produced a basis of morphisms between such objects that are called Light Leaves. I am fascinated by them. On the one hand, it is because of them that one can actually compute in Soergel bimodule-land, and on the other, they have some very rich combinatorial structure that is slowly unearthing. My favorite subjects are diagrammatical category theory, categorical braid group actions, modular representations of finite or algebraic groups, Kazhdan-Lusztig theory, categorifications and knot theory. Very nice.

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September 20, 2017
For Mathematicians / Organization of conferences

Coorganizer (with Aaron Lauda and Joshua Sussan) of the session “Symmetry in algebra, topology, and physics” in the Math Congress of the Americas

Coorganizer (with Aaron Lauda and Joshua Sussan) of the session "Symmetry in algebra, topology, and physics" in the Math Congress of the Americas MCA 2017 The second Mathematical Congress of the Americas…

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July 20, 2017
For Mathematicians / Papers and preprints

Indecomposable Soergel bimodules for Universal Coxeter groups

joint with Ben Elias ; with an appendix by Ben Webster,  Transactions of the American Mathematical Society 369 (2017), 3883-3910. We introduce the multicolored Temperley-Lieb 2-category. Using it, we find the explicit numbers for which "Soergel's conjecture in positive characteristic for Universal Coxeter systems" fail.

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June 1, 2017
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For Mathematicians / Future talks and trips

Invited talk in the Conference “La resolución de Problemas, una competencia transversal”, 26th May 2017, Santiago, Chile.

Invited talk in the Conference "La resolución de Problemas, una competencia transversal", 26th May 2017, Santiago, Chile. SEMINARIO: "LA RESOLUCIÓN DE PROBLEMAS: UNA COMPETENCIA TRANSVERSAL EN EL CURRÍCULO ESCOLAR" 25…

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May 26, 2017
For Mathematicians / Organization of conferences

“Quinquagenary, Faculty of Sciences, University of Chile”, 9-11 December, 2015, Santiago, Chile. (I invited ten Nobel prize recipients to this conference).

"Quinquagenary, Faculty of Sciences, University of Chile", 9-11 December, 2015, Santiago, Chile. (I invited ten Nobel prize recipients to this conference).

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December 9, 2015
For Mathematicians / Organization of conferences

Primer Congreso Internacional Aproximaciones Experimentales a la Interacción Social, 14-16 January 2015, Valparaíso, Chile.

Primer Congreso Internacional Aproximaciones Experimentales a la Interacción Social, 14-16 January 2015, Valparaíso, Chile. Congreso Internacional, Aproximaciones Experimentales a la Interacción Social Organizan: RIA Redes Interactivas de Aprendizaje Fecha: 14 al 16 de…

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January 14, 2015
For Mathematicians / Papers and preprints

Light leaves and Lusztig’s conjecture

Advances in Mathematics (2015) 772-807. I introduce the double leaves basis and with it I prove that Lusztig's conjecture reduces to a problem about the light leaves. Using the result in Section 4.3 of this paper Geordie Williamson disproved Lusztig's conjecture! The counterexamples grow exponentially in the Coxeter number. Here is Geordie's paper  

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January 1, 2015
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For Mathematicians / Papers and preprints

Standard objects in 2-braid groups

Joint with Geordie Williamson, Proceedings of the London Mathematical Society 109 (2014), no. 5, 1264-1280. We introduce the concept of Δ-exact complexes for any Coxeter system. With that, we establish the existence of analogues of standard and costandard objects in 2-braid groups, thus proving the conjecture that Rouquier stated in the ICM 2006. This result was a key step for the proof by Elias and Williamson of Kazhdan-Lusztig conjectures

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January 1, 2014