Here is the first (and only until now) research article I did about these ideas, with Jorge Soto-Andrade On the role of corporeality, affect and metaphoring in Problem Solving. We…
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.
Invited talk in University of Sydney algebra seminar, 11th August 2017 University of Sydney Algebra Seminar Recent and forthcoming seminars The Algebra Seminar is held on Fridays from 12 to…
Plenary talk in "Representation Theory Day in Québec City", 29th July 2017. Schedule (Vachon building, Room 3840) All talks will be held in the Alexandre-Vachon building, Room 3840; Coffee will be…
Invited talk in "Math Congress of the Americas" in the session "Representations of Lie algebras", 28th July 2017.
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…
Invited stay in Sydney University, invited by Geordie Williamson, 5th July-25th August.
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.
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…
Master student September 2016 – Present
"Quinquagenary, Faculty of Sciences, University of Chile", 9-11 December, 2015, Santiago, Chile. (I invited ten Nobel prize recipients to this conference).
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…
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
Orderable groups, 1-5 September 2014, Cajón del Maipo, Chile Minicourses: 1) Ordered groups and topology. Adam Clay (U. Québec / Montréal). 2) Orderable group actions and the deep-fall property. Igor Mineyev (Illinois…
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