Conférence pour les masters OcciMath

15 janv. 2026, 09:00 → 16 janv. 2026, 17:00 Europe/Paris

La fédération OcciMath avec les département de mathématiques de l'Université de Montpellier et de l'Université Paul Sabatier Toulouse III organisent la deuxième conférence pour les masters de mathématiques de la région Occitanie. 

Cette conférence aura lieu les jeudi 15 et vendredi 16 janvier 2026 à l'Institut de Mathématiques de Toulouse (amphi Schwartz). Ces journées seront l'occasion de 3 mini-cours en anglais de 2 h 30 d'initiation à des domaines de recherche actifs sur la région Occitanie.

Les intitulés des cours prévus sont les suivants: 

• "A fundamental tool in Random Matrix Theory: the Cauchy-Stieltjes transform" par Mireille Capitaine (IMT)
• "Bézout's theorem and applications" par Enrica Floris (IMT)
• "An Introduction to Viscosity Solutions for Hamilton–Jacobi Equations" par Jessica Guérand (IMAG)

 

Des résumés sont disponibles sous les onglets "Liste des contributions." 

Les inscriptions sont libres mais obligatoires. Elles se font via l'onglet inscription avant le 15 novembre 2025. Les étudiant.e.s  de montpellier peuvent bénéficier d'un soutien financier pour participer à la conférence. Cette demande doit se faire en envoyant un mail à matthieu.hillairet@umontpellier.fr

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The fédération OcciMath together with  the "département de mathématiques" of Université de Montpellier and Université Paul Sabatier Toulouse III are organizing the second conference for mathematics masters in the Occitanie region. 

The conference will take place on thursday 15 and Friday 16 in January 2026 at the Institut de Mathématiques de Toulouse (amphi Schwartz). These days will feature 3 mini-courses in english during 2 h 30 thought as introduction to research fields active in région Occitanie.

The course titles are as follows: 

• "A fundamental tool in Random Matrix Theory: the Cauchy-Stieltjes transform" by Mireille Capitaine (IMT)
• "Bézout's theorem and applications" by Enrica Floris (IMT)
• "An Introduction to Viscosity Solutions for Hamilton–Jacobi Equations" by Jessica Guérand (IMAG)

 

Abstracts are available under the "List of contributions" tab. 

Registration is free but mandatory. They can be made via the registration tab before November 15. Students from Université de Montpellier can benefit financial support from Fédération to participate to the conference. All demands must be sent by email to matthieu.hillairet@umontpellier.fr.

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Le Comité d'oganisation / Organizing committe:

• Elodie Brunel-Piccinini (IMAG)
• François Chapon (IMT)
• Grégory Faye (IMT)
• Matthieu Hillairet (IMAG)
• Hélène Mathis (IMAG)
• Nicolas Meyer (IMAG)
• Joao-Pedro Pinto dos Santos (IMAG)
•  Barbara Schapira (IMAG)
• François Vilar (IMAG)
• Maxime Wolff (IMT)

 

jeu. 15 janvier

1 A fundamental tool in Random Matrix Theory: the Cauchy-Stieltjes transform - Part 1

We will introduce the so-called Cauchy-Stieltjes transform of a probability measure on the real line and present some of its fundamental properties. Then, we will explain how this analytic tool can be used to establish asymptotic spectral properties of random Hermitian matrices when the dimension goes to infinity.

Orateur: Prof. Mireille Capitaine (IMT)

15:30 Pause Café

2 Bézout's theorem and applications - Part 1

Bézout's theorem for plane curves states that two irreducible curves in the complex projective plane of degree d and e meet in exactly de points counted with multiplicity.
In these lectures we will explain the statement of the theorem, give some applications and generalizations and give some elements of the proof.

Orateur: Prof. Enrica Floris (IMT)

ven. 16 janvier

3 An Introduction to Viscosity Solutions for Hamilton–Jacobi Equations - Part 1

This mini-course provides an introduction to viscosity solutions, a weak notion of solution introduced by Crandall and Lions. This framework is particularly well suited for Hamilton–Jacobi equations, where classical solutions may fail to exist. We will focus on first-order Hamilton–Jacobi equations, presenting the main ideas, illustrating them with examples and applications such as traffic flow modeling and optimal control, and discussing the well-posedness of these equations.

Orateur: Mme Jessica Guerand (IMAG)

11:00 Pause Café

4 A fundamental tool in Random Matrix Theory: the Cauchy-Stieltjes transform - Part 2

We will introduce the so-called Cauchy-Stieltjes transform of a probability measure on the real line and present some of its fundamental properties. Then, we will explain how this analytic tool can be used to establish asymptotic spectral properties of random Hermitian matrices when the dimension goes to infinity.

Orateur: Prof. Mireille Capitaine (IMT)

5 Bézout's theorem and applications - Part 2

Bézout's theorem for plane curves states that two irreducible curves in the complex projective plane of degree d and e meet in exactly de points counted with multiplicity.
In these lectures we will explain the statement of the theorem, give some applications and generalizations and give some elements of the proof.

Orateur: Prof. Enrica Floris (IMT)

15:30 Pause Café

6 An Introduction to Viscosity Solutions for Hamilton–Jacobi Equations - Part 2

This mini-course provides an introduction to viscosity solutions, a weak notion of solution introduced by Crandall and Lions. This framework is particularly well suited for Hamilton–Jacobi equations, where classical solutions may fail to exist. We will focus on first-order Hamilton–Jacobi equations, presenting the main ideas, illustrating them with examples and applications such as traffic flow modeling and optimal control, and discussing the well-posedness of these equations.

Orateur: Mme Jessica Guerand (IMAG)