• 2018-02-20

    Stéphanie Schanck, Véronique Bazier-Matte, Nadia Lafrenière, Mélodie Lapointe, Pauline Hubert and Élise Vandomme participating in the movie “Faces of Women in Mathematics”

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    Pavillon President-Kennedy, UQAM

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    ARTA III : Advances in representation theory of algebras (2014)

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    Mathematics in Marseille with Mark Haiman, Cédrik and François Bergeron

  • RS, Adriano Garsia
La Jolla, CA

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    Mathematics at the beach, Richard Stanley and Adriano Garsia (2003)

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    Mathematics at the bar in Banff with Adriano Garsia and Nantel Bergeron

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    Mountain mathematics with Francois and Nantel Bergeron, Jennifer Morse and Adriano Garsia

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    Christophe Reutenauer and Toni Machi, Bibbiena 2008

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    Xavier Viennot, Nantel Bergeron, Christophe Reutenauer, near Alghero 1988

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    Members of the LACIM in the early 90

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    Denis Thérien, Marcel-Paul Schützenberger, Oberwolfach 1986

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    Thesis defense by Jérôme Fortier

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    Gilbert Labelle and Christophe Reutenauer at Pierre Leroux’s house, Longueuil, early 2000

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    Christian Stump, Nicolas Thiéry, Franco Saliola, Florent Hivert

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    Richard Stanley at the LACIM seminar

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    Sage days at LACIM

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    Symposium on Coxeter groups

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    Sébastien Labbé, Marco Robado, Srecko Brlek, Louis-François Préville-Ratelle, Alejandro Morales, Mathieu Guay-Paquet, Vivien Ripoll

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    Sage days

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    LaCIM seminar

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    La choucroute du patron

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    La choucroute du patron

Seminars

The Shapiro-Shapiro ConjectureFriday, 14 December 2018, 13:30

Kevin Purbhoo (Waterloo)

Abstract: In the 1880's, Schubert solved a problem about enumerating subspaces of $\mathbb{C}^n$ that have non-trivial intersections with other subspaces, beginning the study of what is now known as Schubert calculus. Nowadays, Schubert's problem is usually reinterpreted as a calculation in the cohomology ring of the Grassmannian, and this perspective has been vastly generalized. However, if we change $\mathbb{C}^n$ to $\mathbb{R}^n$, the cohomology perspective no longer works and the situation is less well understood. In 1993, Boris and Michael Shapiro formulated a remarkable conjecture about real solutions to Schubert problems. It was proved in 2005 by Mukhin, Tarasov and Varchenko, using high powered machinery from quantum integrable systems. Since then, many applications and generalizations have been found or conjectured. In this talk, I will tell the story of the Shapiro-Shapiro conjecture, and then tell you about a new theorem (joint work with Jake Levinson), a not-so-obvious generalization. Our result is independent of Mukhin-Tarasov-Varchenko, implies the conjecture, and naturally lends itself to a much more intuitive proof.