## 2022 Winter events

##### 09/01-14/01 - Recent development in Link Homology

*Organizers: Anna Beliakova (Universität Zürich)**, Krzysztof Putyra (Universität Zürich), Louis-Hadrien Robert (University of Luxembourg).*

*Link homology theories emerged about 20 years ago with the celebrated Khovanov homology and Heegaard–Floer homology. These theories categorify respectively the Jones polynomial and the Alexander polynomial, the two most famous polynomial link invariants. These theories are likely to become an essential building block in the seek for a 3+1 quantum field theory (but many hard steps are still to be accomplished).*

Since then many developments occured and generalizations of these theories have been defined and studied. We appear to be at a crucial moment: on the one end, relationships between these different theories is more and more understood; on the other end, many new ideas have come to light in the last five years: y-ification, geometric approach via Hilbert schemes of points, Hopfological algebra, foam evaluation, etc. These new ideas raise new questions and establish connections with other mathematical fields such as (derived) algebraic geometry, homotopy theory, Schubert calculus, combinatorics, etc, while the hope to obtain a mathematical definition of a 3+1 quantum field theory is growing.

*The aim of this workshop is to facilitate communication between mathematicians and theoretical physists investigating all the emerging directions coming from link homology theories. The hope is to get a better understanding of how these new ideas relate with one another and to try to clear the path to the quest of categorified 3-manifold invariants.*

##### 16/01-21/01 From Coadjoint Orbits to Black Holes

*Organizers: Anton Alekseev (UNIGE), Pranjal Nayak (UNIGE), Julian Sonner (UNIGE).*

*This conference aims to bring together physicists and mathematicians interested in low-dimensional examples of holographic dualities, the orbit method and their interplay via the quantization of coadjoint orbits of the Vi- rasoro group. The scope of this event encompasses two and three dimensional gravitational theories and their description via ensembles of strongly correlated quantum systems. These systems share the property of having an IR description that can be understood via the quantization of the coadjoint orbits of the Virasoro group and thus constitute a fertile ground for the interaction between physicists and mathematicians interested in these structures.*

##### 30/01-04/02 Winter School in Mathematical Physics 2022

*Organizers: Anton Alekseev (UniGe), Alberto Cattaneo (UZH), Giovanni Felder (ETH Zürich), Maria Podkopaeva (IHES), Thomas Strobl (U. Lyon 1) and Andras Szenes (UniGE).*

##### 06/02-11/02 Differentiable Stacks, Poisson geometry and related geometric structures

*Organizers : Henrique Bursztyn (IMPA), Rui Loja Fernandes (University of Illinois), Marco Gualtieri (University of Toronto), Jiang-Hua Lu (University of Hong-Kong).*

*Recent days have seen a rapid developments on shifted Poisson and symplectic structures on (derived) differentiable or algebraic stacks. A differentiable stack is, roughly speaking, a Lie groupoid up to Morita equivalence, and the stack represented by a symplectic groupoid of a Poisson manifold naturally has a 1- shifted symplectic structure. There have also been remarkable recent advances in other geometries, such as Dirac geometry and generalized complex geometry, that generalize Poisson geometry and have Lie groupoids and Lie algebroids at their cores. Many basic concepts and constructions in these geometries can be rephrased using the language of differential stacks, and such reformulations put these geometric structures in vastly new perspectives and establish further connections with other fields of mathematics such as algebraic geometry, deformation theory and high category theory.*

*We propose a workshop with at most 40 participants, centered at Differentiable stacks, Poisson geometry and Lie groupoids, but also covering other related geometrical structures. More concretely, we propose to cover the following specific topics.*

*Integrations of Poisson and Dirac structures**Generalized complex geometry and mirror symmetry**Multiplicative structures on Lie groupoids and stacks**Shifted symplectic geometry**Higher Lie groupoids and higher gauge theory*

*We plan to organize the workshop around these five different topics, each day devoted to a main theme. Each day will start with a keynote lecture by a top researcher in the field, followed by a problem session run by a junior researcher. The afternoon sessions will be a mix of talks by by senior researchers and some of the most promising young researchers in these fields. Senior speakers will be asked to focus mostly on open problems and to discuss major research directions.*

##### 13/02-18/02 - Workshop in Statistical Mechanics 2022

*Organizer: S. Smirnov (UniGe)*

##### 20/02-25/02 Vertex Algebras and Poisson Geometry

*Organizers: Anton Alekseev (UNIGE), Leonid Rybnikov (NRU HSE Moscow)*

##### 27/02-04/03 Workshop on Spin Glasses

*Organizers: David Belius (University of Basel), Erwin Bolthausen (University of Zurich), Giuseppe Genovese (University of Basel)*

* Few other branches of statistical mechanics are pushing the frontiers with other sciences as the theory of spin glasses. In this workshop the focus will be on the newest trends in the mathematical theory of spin glasses and its application to high dimensional statistics and machine learning. Topics of central interest include: pure states in spin glasses and their relation to energy landscapes, Thouless-Andersson-Palmer equations, approximate message passing methods, phase transitions in high dimensional statistical inference and optimization algorithms, non-convex optimisation of high dimensional landscapes, approximate message passing methods, neural network models and perceptrons. *

## 2022 Summer events

##### 29/05-03/06 - Workshop on Network Non-Locality

*Organizers: Nicolas Brunner (UNIGE), Nicolas Gisin (UNIGE), Renato Renner (ETH Zürich)*

*Non-locality is by now a well established field, both within foundations of quan- tum physics and in quantum information science. However, non-locality in networks is a new burgeoning field, triggered by ”old” (Bell) nonlocality and by the prospect of future quantum network that will connect quantum proces- sors and deliver, among others, informationally secure cryptography. The main new ingredient is the assumption that distant sources of entanglement are in- dependent. This is a very natural assumption, however it drastically changes the problem of characterizing which probability distributions are local, quan- tum and post-quantum. Indeed, this independence assumption implies that the problem is no longer convex, hence far more difficult and interesting.*

*Finding quantum distributions that are ”network nonlocal” is far from sim- ple, especially if one likes them to be noise-resistant and thus experimentally friendly. Interestingly – and in strong contrast to Bell nonlocality – there are cases without inputs. This should lead to quantum randomness (i.e. random outputs) without any inputs! Furthermore, the general characterization of net- work nonlocal probability distributions, only restricted by No-Signaling & In- dependence (i.e. by the NSI principle), is a fascinating research topic that goes beyond quantum physics.*

##### 05/06-10/06 - Helvetic Algebraic Geometry Seminar (HAGS) 2022

*Organizers: Rahul Pandharipande (ETH Zürich) and Andras Szenes (UniGe)*

##### 03/07-08/07 Large Charge in Les Diablerets

*Organizers: Luis Alvarez-Gaume (SCGP), Simeon Hellerman (Kavli IPMU), Domenico Orlando (INFN Sezione di Torino), Susanne Reffert (University of Bern)*

##### 21/08-26/08 Gauged maps, Vortices and their moduli

*Organizers: Nuno Romão (University of Augsburg), Eduardo González (University of Massachusetts), András Szenes (University of Geneva)*

*A gauged map u is a generalization of a morphism Y → X between almost complex manifolds that takes into account a given symmetry under some group G on the target X. It is natural to consider objects that are invariant under this symmetry, assumed Hamiltonian, and a most sensible extension is to promote u to be a section of a G-bundle with base Y and fiber X. In gauge theory (on Y), this situation is very familiar when X is a representation space for G, but there is no need to restrict to linear G-actions.*

*The most central objects in this context are the moduli spaces parametriz- ing all gauged maps up to symmetry within a fixed homotopy class (under a suitable stability condition). They carry intrinsic geometry and have featured in important constructions from mathematical physics to enumerative geometry. Recently, they have been examined from viewpoints such as geometric quantization, localization in supersymmetric gauge theories, geometric group theory, and algebraic stacks. The range of applications has also been diversified, in their avatars as spaces of vortices, stable pairs or quasi-maps — e.g. in the exploration of new dualities in QFT, in quantum K-theory, and in the context of quantum integrable systems.*

*This workshop congregates gauge theorists and algebraic geometers to discuss some of these developments and future prospects. A diverse program of research talks will be complemented by three minicourses:*

*1. Quillen metrics and applicationsJean-Michel Bismut (Université Paris-Sud, France)*

*2. Introduction to Θ-stratifications of moduli spaces Daniel Halpern-Leistner (Cornell University, USA)*

*3. Vortices and monopoles in 3d SUSY gauge theories Justin Hilburn (Perimeter Institute, Canada)*

##### 28/08-02/09 Algebra, Topology and the Grothendieck-Teichmüller group

*Organizers: Anton Alekseev (UNIGE), Thomas Willwacher (ETH Zürich)*

##### 04/09-09/09 Young Group theorists workshop: exploring new connections

* Organizers: Anton Alekseev (UNIGE), Donna Testerman (EPFL), Rebecca Waldecker (Martin-Luther-Universität Halle-Wittenberg)*

*This is a five day workshop with the uniting theme « Groups and group actions ».** Each day focuses on a specific topic and will be planned by an experienced colleague together with early stage researchers*

*The topics are:*

*Permutation groups**Linear groups and maximal subgroups**Computational methods in group theory**The Classification of the Finite Simple Groups and some applications**Generation in finite and profinite groups and probabilistic methods in group theory*

*Our motivation for these topics stems from recent applications of group actions to various questions in algebra, geometry, number theory and computer science. The topics are approachable for young researchers via the theory of permutation groups and matrix groups, and there is the possibility to get involved in ongoing projects as well as exploring genuinely new open questions. We cover the theoretical and the applied side and also include computational methods because this area has seen some impressive progress on hard problems recently.*

*A typical theme day will start with a long introductory lecture in the morning, with much room for discussion and questions, and then in the afternoon we will go deeper into the topic, for example with shorter, more specialised talks by early or mid stage researchers, with a poster session or open discussion groups where potential projects and work in progress are shared. Moreover, we plan to have a majority of female speakers and an overall diverse and well-balanced group of participants, with many opportunities for exchanging experiences and informal coaching.*

##### 25/09-30/09 Let’s talk about outreach

*Organizers: Pierre-Alain Cherix (UNIGE), Shaula Fiorelli (UNIGE), Joana Mailler (UNIGE), Elise Raphael (UNIGE)*

*We propose a conference on outreach bringing together its different actors and its different aspects. The program will be divided into three parts:*

*1. Outreach actors: who does outreach ? : On the occasion of this con- ference, various actors of outreach, YouTubers, researchers, science center managers, will come to talk about their profession and their methods.*

*2. The outreach, what’s that all about ? : Through talks and working sessions, participants will be able to familiarize themselves with research in outreach which is in its beginning. We will start by understanding how a theoretical reflection on practices can change the way we present concepts, and then we will think about which theoretical frameworks to put in place to analyze our practices;*

*3. Getting hands-on : Participants will be invited to experience outreach as learners during some workshops. Material will also be available on an ongoing basis so that participants can experience it whenever they wish. In addition, there will be work sessions specifically dedicated to the creation of new activities.*