Junior Math Days 2025

Dec 1, 2025, 9:00 AM → Dec 3, 2025, 3:00 PM Europe/Rome

SISSA

Chiara Trifone, Davide Donati (SISSA, Trieste), Matteo Zanardini (SISSA), Lorenzo Cortelli (SISSA)

The Junior Math Days are an occasion for Master’s students to get in touch with the mathematical research environment at SISSA.

 

The 2025 edition will take place on 1-2-3 December 2025. 

 

Selected participants can spend three days in the stimulating environment of SISSA, taking part in several planned activities. The program includes:

• introductory talks given by professors and post-docs about their research
• informal meetings with students to discuss their work and experience as PhD students

Other activities to experience life in Trieste include:

• a welcome dinner
• a visit to the city 

A provisional schedule of the event is available in the Timetable section. Speakers and titles of their talks will be announced before the beginning of the event.

 

Please read the How to apply section before registering to the event. Registrations will close on 7^th November 2025, at 1pm (Central European Time time). 

 

For further information, feel free to send us an email at jmd (‘at’) sissa.it.

 

The Junior Math Days are organized by SISSA PhD students, in collaboration with SISSA Mathematics Area, Comitato Unico di Garanzia (CUG), and IGAP.

 

 

        

Monday, December 1

9:15 AM → 10:15 AM Antonio Lerario-"How many zeroes of a random polynomial are real? A probabilistic approach to real algebraic geometry"

In this talk I will discuss a probabilistic approach to some questions in classical real algebraic geometry, like the study of the number of real  zeros of real polynomial systems, or the study of the number and relative position of the connected components of a plane real algebraic curve. The main idea is to insist on the measure theoretic flavor of the notion of “generic” from complex algebraic geometry, by turning the space of polynomials into a probability space and studying the expectation of such topological quantities.

10:15 AM → 11:10 AM Andrea Cangiani-"Reliable Numerical Modelling with Partial Differential Equations"

Mathematics is increasingly becoming an indispensable tool for understanding complex phenomena, ranging from the regeneration of damaged bone tissue to the drift of Earth’s continents. Thanks to modern algorithms and the growing availability of computational power, it is now possible to perform highly accurate numerical simulations of realistic models describing such processes.
In this talk, I will survey recent advances in the numerical analysis of partial differential equation based models, with a particular emphasis on techniques that ensure the reliability of computations, producingnumerical solutions equipped with rigorous guarantees on their accuracy.

11:10 AM → 11:40 AM Coffee break

11:40 AM → 12:40 PM Barbara Fantechi

12:40 PM → 1:35 PM Felix Rott- "Alexandrov geometry and nonsmooth Lorentzian geometry"

We give a beginner friendly introduction to Alexandrov geometry. We recall some basic concepts from Riemannian geometry and give an idea of how they can be abstracted to a setting beyond manifolds. We state Toponogov's Theorem on triangle comparison and the associated globalisation theorems. We conclude with a brief outlook on how this successful theory can be applied in Lorentzian signature.

1:35 PM → 3:00 PM Lunch break

3:00 PM → 4:00 PM Meeting with PhD students

4:00 PM → 6:00 PM Tour of the city center

8:00 PM → 9:00 PM Social Dinner

Tuesday, December 2

9:15 AM → 10:15 AM Davide Riccobelli-"Continuum Mechanics @ SISSA mathLab"

In this talk, we will present the main research directions in mathematical modelling and continuum mechanics developed at SISSA. A non-exhaustive list includes shape-morphing structures inspired by nature, fracture in soft materials, microswimming, active matter, and mechanobiology.

We will provide an overview of current and future research projects. To offer a more detailed perspective, we will also discuss some recent results in cancer modelling and personalized medicine.

10:15 AM → 11:10 AM Nicola Gigli- "Introduction to optimal transport"

I will give an overview of the proof of the celebrated theorem by Brenier about existence of optimal maps in the Euclidean setting.

Interestingly, this deep result will unwrap in front of our eyes once we identify a few key concepts, such as that of c-cyclical monotonicity and c-concavity.

11:10 AM → 11:40 AM Coffee break

11:40 AM → 12:40 PM Tommaso Rossi-"Regularity of sub-Riemannian geodesics"

Sub-Riemannian geometry is a generalization of Riemannian geometry in which a metric is defined only on a subset of preferred directions, called a distribution. For curves tangent to the distribution, one can define their length, and the curves that minimize length are called sub-Riemannian geodesics. In this talk, I will discuss the regularity of sub-Riemannian geodesics: whereas geodesics in Riemannian geometry are always smooth, sub-Riemannian geodesics are not always smooth. I will also present examples showing that sub-Riemannian geodesics can branch. This is based on joint work in progress with A. Schiavoni Piazza and A. Socionovo.

12:40 PM → 1:35 PM Shulamit Terracina

1:35 PM → 3:00 PM Lunch break

3:00 PM → 4:15 PM Meeting with PhD students

4:15 PM → 4:45 PM Coffee break

4:45 PM → 5:45 PM Meeting with PhD students

Wednesday, December 3

9:15 AM → 10:15 AM Ilya Chevyrev-"Stochastic and rough analysis"

Stochastic analysis is an area of mathematics that aims to make rigorous sense and study properties of differential equations with random functions. Such equations appear frequently in mathematical physics, finance, and biology. Random functions are often very rough and the solution theory of stochastic differential equations falls outside the scope of classical calculus, so new tools are needed to study them. In this talk, I will describe one of the tools, called rough analysis, that has been developed in the past two decades and which has significantly extended the scope of “classical” stochastic analysis.

10:15 AM → 11:10 AM Mikhail Bershtein- "Quantum groups"

The theory of quantum groups developed in the 1980s from attempts to understand structures that appear in integrable models of quantum field theory and statistical physics.  Remarkably, almost immediately, quantum groups found applications in representation theory, low-dimensional topology, enumerative geometry, and many other areas of mathematics.  In the talk, I will review some basic ideas, examples, and applications of quantum groups.

11:10 AM → 11:40 AM Coffee break

11:40 AM → 12:40 PM Jacopo Stoppa-"Special Lagrangian submanifolds and the Thomas-Yau conjecture"

In the first part of the talk, starting from basic notions, I will introduce special Lagrangian submanifolds, due to Harvey and Lawson. These play an important role in the calculus of variations and in string theory. Around the year 2000, R. Thomas and S.-T. Yau proposed a conjectural criterion for the existence of a special Lagrangian submanifold in a suitable fixed isotopy class. In the second part of the talk I will sketch the current viewpoint of this conjecture, due to D. Joyce and Y. Li, mentioning some positive results for a class of examples with toric symmetry.

12:40 PM → 1:35 PM Marcello Porta-"Quantum Statistical Mechanics"

In this talk I will discuss the rigorous study of problems in quantum statistical mechanics, motivated by condensed matter physics. I will focus on the integer quantum Hall effect, a paradigmatic example of topological transport phenomenon, which motivated a lot of research both in physics and in mathematics in the last 40 years. I will give an introduction to the phenomenon, to its mathematical formulation, and to some of the mathematical methods used in its rigorous analysis.

1:35 PM → 2:35 PM Lunch break