# IKUR QUANTUM TALKS: Professor Jan Philip Solovej

Date: Wed, Jan 24 - Fri, Jan 26 2024

Location: UPV/EHU (Leioa) | San Telmo Museoa | DIPC

Speakers: Professor Jan Philip Solovej

Via a joint organisation involving the DIPC, BCAM and EHU Quantum center, **Professor Solovej, currently the president of the European Mathematical Society** (attached the bio), is going to make a **series of talks in the Basque country, from January 24th to January 26th.**

**1. Wednesday 24/01/2024, 11:30-12:30, at the UPV/EHU (Leioa), Salón de Grados.**

**TITLE: On dilute quantum gases **

**ABSTRACT:** I will give an overview of the mathematical description of quantum many-body systems, in particular, the ground states of gases of many interacting identical particles. Such systems can be experimentally implemented in (very) cold atomic gases. The atoms are either bosons (e.g. Lithium7) or fermions (e.g., Lithium6). Bosons in three dimensions at very low temperature form Bose-Einstein condensates (although we do not know how to show this rigorously) and become superfluid. I will discuss recent rigorous results on the ground state energy of Bose gases in the limit when they become dilute. I will discuss both 1,2 and 3 dimensions. The asymptotic formula for the ground state energy in 3 dimensions, the celebrated Lee-Huang-Yang formula, is in agreement with the theory of superfluidity and thus validates aspects of the theory. I will also briefly review some results about Fermi gases. This is based on work with Agerskov, Fournais, and Reuvers.

**Online seminar on https://www.youtube.com/ztffctehu**

** https://ehutb.ehu.eus/live/58c6ba0bf82b2b093f8b456a**

**2. Thursday 25/01/2024, 19:00-20:00, public talk at San Telmo Museoa in Donostia.**

**TITLE: **From Atoms to Stars: The Universe according to Pauli.

see **https://www.santelmomuseoa.eus/m/agenda-detalle.php?id=18553&lang=eu **

**3. Friday 26/01/2024, 10:00-11:00 am, Seminar Room of the DIPC**

**TITLE: **The mathematics of the periodic table of the elements

**ABSTRACT:** The elements are grouped in the periodic according to their chemical properties. Elements with similar properties form the columns in the periodic table. The Aufbau principle or Madelung rule gives a phenomenological explanation for the structure of the periodic table. In this talk I will discuss two mathematical results relating to the periodic table. To make general mathematical statements I will allow myself to consider atoms with atomic number much larger than those that exist in nature. The non-relativistic quantum mechanical description of atoms can be studied mathematically for arbitrarily large atomic number. I will ask the following two questions. Does the periodic structure persist for arbitrarily large atoms? Is the Aufbau principle still valid for large atoms? The answer to the second question is no. The Aufbau Principle fails for large atoms. The first question is more difficult and I do not know the answer in general. I will, however, show that in a certain mean field model of atoms there is an exact periodic behavior in the limit of infinitely large atoms. This is based on work with Bjerg, Fournais, and Hearnshaw.

## Organizers:

Jean-Bernard Bru (BCAM), Enrique Rico Ortega (UPV/EHU), Feza Giedke (DIPC)

## Confirmed speakers:

**Professor Jan Philip Solovej**

Jan Philip Solovej was born June 14, 1961 in Copenhagen Denmark. He received his Phd from Princeton University in 1989. After several postdoctoral positions Jan Philip Solovej became an assistant professor at Princeton University from 1991-1995. From 1995 to 1997 he was a professor at Aarhus University in Denmark and since 1997 a professor at the University of Copenhagen. Professor Solovej has had an ERC Advanced grant from 2013-2018 and currently is the head of a research center for the Mathematics of Quantum Theory (QMATH) funded by the VILLUM foundation. He was awarded the Henri Poincaré prize from the international association of mathematical physics (IAMP). Professor Solovej has had numerous administrative position and is currently the president of the European Mathematical Society. His research focuses on the structure and stability of quantum matter from atoms to condensed matter systems.

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