In this talk we present a proof of the Kodaira's theorem that gives a sufficient condition on the existence of an embedding of a Kahler manifold into CPn. This proof is based on the Kodaira Vanishing theorem, using a sheaf-cohomological translation of the embedding conditions. לאירוע הזה יש שיחת וידאו. הצטרף: https://meet.google.com/mcs-bwxr-iza

Let X be a complex manifold and let M be a meromorphic connection on X with poles along a normal crossing divisor D. Levelt-Turrittin theorem asserts that the pull-back of M to the formal neighbourhood of a codimension 1 point in D decom poses (after ramification) into elementary factors easy to work with. This decomposition may not hold at some other points of D. When it does, we say that M has good formal decomposition along D. A conjecture of Sabbah, recently proved by Kedlaya and Mochizuki independently, asserts roughly the

Title: Towards Chabauty-Kim loci for the polylogarithmic quotient over an arbitrary number field Abstract: Let K be a number field and let S be an open subscheme of Spec O_K. Minhyong Kim has developed a method for bounding the set of S-valued points on a hyperbolic curve X over S; his method opens a new avenue in the quest for an "effective Mordell conjecture". But although Kim's approach has lead to the construction of explicit bounds in special cases, the problem of realizing the potential effectivity of his methods remains a difficult and beautiful open problem.

I will discuss in the talk David Nadler’s “arborealizaton conjecture” and will sketch its proof. The conjecture states that singularities of a Lagrangian skeleton of a symplectic Weinstein manifold could be always simplified to a finite list of singularities, called ``arboreal”. This is a joint work with Daniel Albarez-Gavela, David Nadler and Laura Starkston.

Title: Equidistribution of expanding translates of curves in homogeneous spaces and Diophantine approximation. Abstract: We consider an analytic curve $\varphi: I \rightarrow \mathbb{M}(n\times m, \mathbb{R}) \hookrightarrow \mathrm{SL}(n+m, \mathbb{R})$ and embed it into some homogeneous space $G/\Gamma$, and translate it via some diagonal flow

Speaker: Misha Belolipetsky Title: Arithmetic Kleinian groups generated by elements of finite order Abstract: We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. The proof is based on a generalised Gromov-Guth inequality and bounds for the hyperbolic and tube volumes of the quotient orbifolds. To estimate the hyperbolic volume we take advantage of known results towards Lehmer's problem. The tube volume estimate requires study of triangulations of lens spaces which may be of independent interest.

"Entropy theory for non-amenable groups (part II)"

Consider a sequence of random walks on $\mathbb{Z}/p\mathbb{Z}$ with symmetric generating sets $A= A(p)$. I will describe known and new results regarding the mixing time and cut-off. For instance, if the sequence $|A(p)|$ is bounded then the cut-off phenomenon does not occur, and more precisely I give a lower bound on the size of the cut-off window in terms of $|A(p)|$. A natural conjecture from random walk on a graph is that the total variation mixing time is bounded by maximum degree times diameter squared.

Title: Arithmetic of Double Torus Quotients and the Distribution of Periodic Torus Orbits Abstract: In this talk I will describe some new arithmetic invariants for pairs of torus orbits on inner forms of PGLn and SLn. These invariants allow us to significantly strengthen results towards the equidistribution of packets of periodic torus orbits on higher rank S-arithmetic quotients. An important aspect of our method is that it applies to packets of periodic orbits of maximal tori which are only partially split.

To every topological group, one can associate a unique universal minimal flow (UMF): a flow that maps onto every minimal flow of the group. For some groups (for example, the locally compact ones), this flow is not metrizable and does not admit a concrete description. However, for many "large" Polish groups, the UMF is metrizable, can be computed, and carries interesting combinatorial information. The talk will concentrate on some new results that give a characterization of metrizable UMFs of Polish groups. It is based on two papers, one joint

To every topological group, one can associate a unique universal minimal flow (UMF): a flow that maps onto every minimal flow of the group. For some groups (for example, the locally compact ones), this flow is not metrizable and does not admit a concrete description. However, for many "large" Polish groups, the UMF is metrizable, can be computed, and carries interesting combinatorial information. The talk will concentrate on some new results that give a characterization of metrizable UMFs of Polish groups. It is based on two papers, one joint

Title: Rigidity of higher rank diagonalizable actions in positive characteristic

The (wrapped) Fukaya category of a symplectic manifold is a category whose objects are Lagrangian submanifolds and which contains a wealth of information about the symplectic topology. I will discuss the construction of the wrapped Fukaya category for certain completely integrable Hamiltonian systems. These are 2n-dimensional symplectic manifolds carrying a system of n commuting Hamiltonians surjecting onto Euclidean space. This gives rise to a Lagrangian torus fibration with singularities.