Laboratoire

d'

Algèbre

, de

Combinatoire

et d’

Informatique

Mathématique

Igor Pak donnera le séminaire du LACIM et le Colloque des Sciences Mathématiques du Québec

Ce vendredi 13 septembre 2024, Igor Pak (University of California, Los Angeles) donnera le Séminaire du LACIM et le Colloque des Sciences Mathématiques du Québec (CSMQ).

What is beyond D-finite?

Igor Pak (University of California, Los Angeles)

Séminaire du LACIM (11h, PK-4323)

Résumé. As classes of GFs go, we tend to know more about smaller classes than larger ones, think of the progression from rational to algebraic to D-finite to D-algebraic GFs. The positivity adds another twist on these classes, bringing a host of new problems. In this talk, I will review some classes of GFs that are of interest in Enumerative Combinatorics but remain understudied, emphasising both larger classes and positivity properties.

Polynomial inequalities and combinatorial interpretations

Igor Pak (University of California, Los Angeles)

CSMQ (15h30, PK-5115)

Résumé. In combinatorics, many inequalities can be proved by an explicit injection. Such proofs can be both elegant and insightful. As an application, they give a combinatorial interpretation for the difference between two sides. But what happens to the inequalities when this naive approach doesn’t work? Can you actually prove that this approach is impossible? In the first half of the talk I will give a broad overview or what’s known and give many examples. In the second half, I will discuss how to prove negative results for algebraic inequalities and what does all of that mean. This is joint work with Christian Ikenmeyer.

Le Colloque des Sciences Mathématiques du Québec (CSMQ) est organisé conjointement par le CRM et l’ISM et offre une tribune à des mathématiciennes et mathématiciens de grande réputation, qui sont invités à prononcer des conférences d’intérêt actuel et général, et accessibles à l’ensemble de la communauté mathématique québécoise.