לוח שנה משולב

For d≥4 and p a sufficiently large prime, we construct a lattice Γ≤PSp2d(ℚp), such that its universal central extension cannot be sofic if Γ satisfies some weak form of stability in permutations. In the proof, we make use of high-dimensional expansion phenomena and, extending results of Lubotzky, we construct new examples of cosystolic expanders over arbitrary finite abelian groups. This is joint with with Lukas Gohla.

Protein function is the combined product of chemical and mechanical interactions encoded in the gene. Thus, the function of enzymes relies on finetuning the chemical groups at the active site, but also on large-scale mechanical motions, allowing enzymes to bind to substrates selectively, reach the transition state, and release products. We will discuss recent work aiming to probe directly the linkage between these collective internal motions and the functionality of enzymes, using nano-rheological measurements, AI-prediction of point mutation effects, and physical theory. This work proposes a physical view of enzymes as viscoelastic catalytic machines with sequence-encoded mechanical specifications, which are modulated via long-ranged force transduction.

This talk tells my outlook on the development of electric-field-mediated-chemistry/biochemistry and predicts a vision of its future state.1 The talk discusses applications of oriented electric-fields (OEFs) to chemical and biochemical reactions e.g., Diels  Alder reactions, and reactions of the enzyme Cytochrome P450. As shall be demonstrated, the orientation of the OEF controls reaction-rate (acceleration/inhibition), chemo-selectivity, enantio-selectivity, and solvent effect. This will be followed by showing relevant experimental verifications of the impact of OEF on structure and reactivity.
Subsequently, the talk will outline other ways of generating OEFs, e.g. by use of; pH-switchable charges, ionic additives, water droplets, and so on. I shall further describe the application of static vs. oscillating OEFs to decompose peptide plaques (e.g., Amyloid Plaques in Alzheimer’s disease).
The second part of the talk consists of conceptual principles for understanding and predicting OEF effects, e.g., the “reaction-axis rule”, the capability of OEFs to act as tweezers that orient reactants and accelerate their reaction, etc. Finally, I shall discuss the prospects of up-scaling applications of various OEF-sources to Molar concentrations. The talk ends with the vision that, in the forthcoming years, OEF usage will change chemical education, if not also the art of making new molecules.

A common theme in mathematics is that limits of finite objects are well behaved. This allows one to prove many theorems about finitely approximable objects, while leaving the general case open --- examples for this are Gottschalk's conjecture, Kaplansky's direct finiteness conjecture, and many more. When the topology of the space is somewhat coarse, it becomes very hard to decide whether every object is approximable by finite ones, or whether there exist non-approximable objects. Some of the more famous problems in various fields of mathematics can be framed this way

Arithmetic Topology, first pioneered by Mazur in 1963, draws analogies between number theory and low dimensional topology, primes and knots, and surface and p-adic fields.

On one hand, quantum field theory can be expressed in terms of the geometry and topology of low-dimensional manifolds, on the level of states (via the Atiyah-Segal) and on the level of observables (via the Beilinson–Drinfeld). Thus, as first proposed by Minhyong Kim (in his Arithmetic Chern-Simons Theory), one can try and find arithmetic versions of quantum field theoretic ideas.

In the talk, I will introduce a new general framework for (d 1)-dimensional arithmetic TQFT.

I will explain the classification of such TQFTS for the (1 1)-dimensional case, in terms of Frobenius algebras with some extra structure, this enables us to study pro-p cobordisms and TQFTs for p-adic fields and surfaces at the same time. 

If time permits, I will outline how we use the above to compute a Dijkgraaf-Witten like invariants for G, a finite p-group, to get formulas for counting covers of Surfaces/p-adic fields with Galois group G (these formulas are similar to the ones given by Mednykh for surfaces using TQFTs, and by Masakazu Yamagishi using a more algebraic approach).

The talk is based on joint work with Oren Ben-Bassat.

No prior knowledge of Topological Quantum Field Theory or Arithmetic Topology will be assumed.

The growing success of machine learning across a wide range of domains and applications has made it appealing to be used also as a tool for informing decisions about humans. But humans are not your conventional input: they have goals, beliefs, and aspirations, and take action to promote their own self-interests. Given that standard learning methods are not designed to handle inputs that "behave", it is natural to ask: how should we design learning systems when we know they will be deployed and used in social environments?

As a starting point, I will present the problem of strategic classification, in which users can modify their features (at a cost) in response to a learned classifier in order to obtain favorable predictions. I will then describe some of our work in this field, demonstrating how even mild forms of strategic behavior can dramatically transform the learning problem, and the role game theory can play in addressing some of the new challenges that arise. Finally, I will argue for strategic classification as a framework that can be useful for formally reasoning about learning under user behavior in general, and which holds potential for weaving more elaborate forms of economic modeling into the learning pipeline.