# Prize Lectures

- Vojkan Jaksic
- Val Kelly

Each Prize awarded has an associated lecture given during the Congress. Prize recipient names and scheduled lectures are shown below prize descriptions.

### Prize Descriptions

**Henri Poincaré Prize**

*Sponsored by the Daniel Iagolnitzer Foundation.*

The Henri Poincaré Prize was created in 1997 to recognize outstanding contributions in mathematical physics, and contributions which lay the groundwork for novel developments in this broad field. The Prize is also created to recognize and support young people of exceptional promise who have already made outstanding contributions to the field of mathematical physics.

The prize is awarded every three years at the International Mathematical Physics Congress and in each case, is an award to three individuals (to be exact, the rules say approximately three allowing for exceptional circumstances, at the discretion of the prize committee). Previous Laureates are listed here.

Prize recipients and their associated lectures are shown below.

**IAMP Early Career Award**

Sponsored by Springer.

The prize is awarded at the International Congress of Mathematical Physics (ICMP) in recognition of a single achievement in Mathematical Physics. The prize consists of the sum of 3000€ and is reserved for scientists whose age in years since birth on July 31 of the year of the Congress is less than 35. Previous Laureates are listed here.

The prize recipients and associated lecture are shown below.

**IUPAP Young Scientist Prize**

*Sponsored by the International Union of Pure and Applied Physics.*

The Young Scientist Prizes were established in 2007. The recipients of the awards in a given year should have a maximum of 8 years of research experience following their PhD, and should have performed original work of outstanding scientific quality.

The IUPAP Commission C18 for Mathematical Physics awarded its Young Scientist Prizes for the first time in 2009. Previous Laureates are listed here.

There will be three Prizes awarded. Prize recipients and their associated lectures are shown below.

**Annales Henri Poincaré Journal Prize**

Each year a prize founded by **Birkhäuser** is awarded for the most remarkable paper published in the journal *Annales Henri Poincaré*. The winners of the AHP prize are selected by the Editorial Board. Since 2008, the AHP executive board decided to award also distinguished papers.

For further information and prevous Laureates, read here.

Prize recipients and their associated lectures are shown below.

### Recipients

- Monday, Jul 23 [symposia auditorium]
- 12:00 Semyon Dyatlov (University of California, Berkeley), IAMP Early Career Award Lecture
- Tuesday, Jul 24 [symposia auditorium]
- 11:30 Percy Deift (Courant Institute), Henri Poincaré Prize Lecture
- 16:30 Vadim Gorin (MIT), IUPAP Young Scientist Prize Lecture
- Wednesday, Jul 25 [symposia auditorium]
- 14:00 Giovanni Gallavotti (Sapienza University of Rome), Henri Poincaré Prize Lecture
- Thursday, Jul 26 [symposia auditorium]
- 16:00 Annales Henri Poincaré Journal Prize Ceremony
- Friday, Jul 27 [international i]
- 16:45 Wei-Kuo Chen (University of Minnesota), IUPAP Young Scientist Prize Lecture
- 17:15 Phan Thanh Nam (Ludwig Maximilian University), IUPAP Young Scientist Prize Lecture
- Friday, Jul 27 [symposia auditorium]
- 14:00 Michael Aizenman (Princeton University), Henri Poincaré Prize Lecture
- 16:45 David Damanik (Rice), Annales Henri Poincaré Journal 2014 Prize Lecture
- 17:15 Juliane Rama (Fraunhofer FHR), Annales Henri Poincaré Journal 2015 Prize Lecture
- 17:45 Wojciech Dybalski (Technische Universität München), Annales Henri Poincaré Journal 2016 Prize Lecture

### Lecture Abstracts

- Semyon Dyatlov

University of California, BerkeleyIAMP Early Career Award Lecture**Fractal uncertainty principle and quantum chaos**Fractal uncertainty principle states that no function can be localized close to a fractal set simultaneously in position and momentum. The strongest version so far has been obtained in one dimension by Bourgain and the speaker with recent higher dimensional advances by Han and Schlag. It has applications to spectral gaps in chaotic scattering and to localization and control of high energy eigenfunctions.

More precisely, using the work with Bourgain and earlier work with Zahl, Jin and the speaker proved that on hyperbolic surfaces, the mass of an eigenfunction on an open set is bounded from below independently of the energy. As shown by Jin, these results lead to observability and control for the Schrödinger equation. Another application is the existence of a spectral gap for every convex co-compact hyperbolic surface, which implies local energy decay of waves at high frequency.

- Percy Deift

Courant InstituteHenri Poincaré Prize Lecture**Universality in numerical computation with random data: Case studies and analytical results.**The speaker will discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations, rigorous results, and some speculations about computation in a broader sense.

Joint with C. Pfrang, G. Menon, S. Olver and Thomas Trogdon.

- Vadim Gorin

MITIUPAP Young Scientist Prize Lecture**Telegraph equation from the six-vertex model**I will explain how a second order hyperbolic PDE, known as the telegraph equation, arises in the asymptotic of the height function of a celebrated model of 2d statistical mechanics - the six-vertex (or square ice) model. Homogeneous equation describes the limit shape in the system, and its stochastic inhomogeneous version governs the fluctuations.

- Giovanni Gallavotti

Sapienza University of RomeHenri Poincaré Prize Lecture**Reversibility, Irreversibility, Friction and Nonequilibrium Ensembles in Navier-Stokes equations**A proposal for a theory of equivalent ensembles in nonequilibrium statistical mechanics.

The case of Navier-Stokes fluids. Equivalent irreversible and reversible friction for incompressible, periodic boundary conditions, constant forcing flows in 2/3D.

- Wei-Kuo Chen

University of MinnesotaIUPAP Young Scientist Prize Lecture**Some recent progress on mean field spin glasses.**Spin glass models were initially introduced by theoretical physicists in order to study some strange magnetic behavior of certain alloys. They exhibit several features, such as quenched disorder and frustration, that are commonly shared in many real world problems involving randomized combinatorial optimizations. In this talk, we will discuss some recent progress on the famous Sherrington-Kirkpatrick mean field spin glass as well as its variants. We will explain Parisi's solution to the computation of the ground state energies and give descriptions on the energy landscapes of the models in relation to the computational hardness of the ground state energies.

- Phan Thanh Nam

Ludwig Maximilian UniversityIUPAP Young Scientist Prize Lecture**Nonlinear Gibbs measure and equilibrium Bose gases**Nonlinear Gibbs measure plays an important role in the studies of Euclidean Quantum Field Theory, nonlinear PDEs and stochastic PDEs. I will discuss the natural emergence of this measure as the mean-field limit of bosonic equilibrium states. The talk is based on joint work with Mathieu Lewin and Nicolas Rougerie.

- Michael Aizenman

Princeton UniversityHenri Poincaré Prize Lecture**Emergent structures in statistical mechanics**Equilibrium states of classical and quantum systems can often be understood in terms of spontaneously emergent random geometric structures. Examples of such can be seen in the spontaneous organization of Ising and Potts spins into cliques, whose statistics are given by the Fortuin - Kasteleyn random cluster models, the random current representation of the equilibrium Gibbs states of Ising / phi^4 models, and loop based organization of certain quantum spin chains into spin zero clusters. Uncovering the hidden stochastic geometric features allows insights on the model’s phase structure, and the nature of the correlation functions. For quantum spin chains the loop representations are of relevance for the phenomena of dimerization, the emergence of boundary spin excitations, and in some cases of topological states. Mentioned in the talk will be results based on both old and recent collaborations.

- Annales Henri Poincaré Journal 2014 Prize Lecture
**Schrödinger operators with thin spectra**In the early days of the spectral analysis of Schrödinger operators, the essential spectrum commonly turned out to be an interval, or at least a union of intervals. In the 1980's, new types of spectra were discovered, displaying a Cantor set structure. In this talk we present recent work on Schrödinger operators whose spectra are even thinner, having zero Lebesgue measure, or even zero Hausdorff dimension. The mechanisms leading to these results will be elucidated. This is joint work with Jake Fillman, Anton Gorodetski and Milivoje Lukic.

*Article:*Damanik, D., Fillman, J. & Gorodetski, A. Ann. Henri Poincaré (2014) 15: 1123. https://doi.org/10.1007/s00023-013-0264-6 - Juliane Rama

Fraunhofer FHRAnnales Henri Poincaré Journal 2015 Prize Lecture**Instability of pre-existing resonances in the DC Stark effect**This talk is based on the article:

I. Herbst, J. Rama, "Instability of Pre-Existing Resonances Under a Small Constant Electric Field", Ann. Henri Poincar$\acute{\rm e}$ 16 (2015), 2783 - 2835.

A simple model operator (Friedrichs model) with a pre-existing resonance $r_0$, defined in a dilation or translation analytic framework, is considered. Adding a potential corresponding to a small constant electric field of strength $f>0$ (DC Stark effect) perturbs the pre-existing resonance into (infinitely many) resonances of the resulting operator. It is shown that the pre-existing resonance $r_0$ is unstable in the weak field limit $f\downarrow 0$, in the sense that the new resonances do not converge to $r_0$ as $f\downarrow 0$. In a dilation analytic framework this instability result in the DC Stark effect is in contrast to the AC Stark effect (time-periodic electric field), where the pre-existing resonance is stable in the weak field limit.

*Article:*Herbst, I. & Rama, J. Ann. Henri Poincaré (2015) 16: 2783. https://doi.org/10.1007/s00023-014-0389-2 - Annales Henri Poincaré Journal 2016 Prize Lecture
**Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory for gapped quantum spin systems**We consider translation invariant gapped quantum spin systems satisfying the Lieb-Robinson bound and containing single-particle states in a ground state representation. Following the Haag-Ruelle approach from relativistic quantum field theory, we construct states describing collisions of several particles, and define the corresponding S-matrix. For the purpose of our analysis we adapt the concepts of almost local observables and energy-momentum transfer (or Arveson spectrum) from relativistic QFT to the lattice setting. Our results hold, in particular, in the Ising model in strong transverse magnetic fields. Based on these developments, a general discussion of the problem of asymptotic completeness for gapped quantum spin systems will be given.

Based on joint work with S. Bachmann and P. Naaijkens.

*Article:*Bachmann, S., Dybalski, W. & Naaijkens, P. Ann. Henri Poincaré (2016) 17: 1737. https://doi.org/10.1007/s00023-015-0440-y