# Prize Lectures

Organizers:
• Vojkan Jaksic (McGill University)
• Val Kelly (CMS)
Most Prize Recipients will be announced during the ICMP Opening Ceremony on Monday between 9:00-10:30. When the announcements are made, the recipient information, along with their abstracts and scheduled talks, will appear below.

Papers that have won the Annales Henri Poincaré Prizes have already been announced. There will be a short ceremony on Thursday to present these prizes with lectures on the papers given on Friday.
• IAMP Early Career Award Lecture

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.

Details regarding the recipient, prize lecture title and abstract will be displayed here when the announcements are made during the Monday Prize Ceremony at 09:00-10:30.

• Henri Poincaré Prize Lecture

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.

Details regarding the recipient, prize lecture title and abstract will be displayed here when the announcements are made during the Monday Prize Ceremony at 09:00-10:30.

Each of the three individuals awarded a prize also presents a Prize Lecture.  This time slot will host one of those lectures.

• Henri Poincaré Prize Lecture

See above for description of the Henri Poincaré Prize.

There are three such prizes, each with an associated lecture.  This time slot will host one of those lectures.

• Annales Henri Poincaré Journal Prize Ceremony

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.

Recipients will receive their prize during this ceremony.  Lectures for each of these papers will be presented on Friday at 16:45 - 18:15.

• IUPAP Young Scientist Prize Lectures

The Young Scientist Prizes, sponsored by the International Union of Pure and Applied Physics, 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.  Each Prize winner will present a lecture during this time slot.

Details regarding the recipient, lecture title and abstract, and time and location, will be displayed here when announced.

• Henri Poincaré Prize Lecture

See above for the description of the Henri Poincaré Prize.

There are three such prizes, each with an associated lecture.  This time slot will host one of those lectures.

• David Damanik
Rice
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 FHR
Annales 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

• Wojciech Dybalski
Technische Universität München
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