## Construction of some arithmetically defined compact locally symmetric spaces

## Talk coaching for Postdocs

## New guests at the MPIM

## Some applications of complex Floer theory to topology

I will describe an approach to defining diffeomorphism invariants of low-dimensional manifolds and knots. Morally, these invariants are based on counting solutions to certain equations coming from quantum field theory. However, their rigorous construction relies on ideas from (complex)

symplectic topology and algebraic geometry. Parts of this talk are based on joint work with Ciprian Manolescu and with Ikshu Neithalath, as well as work in progress.

## Period maps, I

## IMPRS seminar on various topics: Period domains

## Lens spaces, group actions, and surgery, II

## Lens spaces, group actions, and surgery, III

## Lens spaces, group actions, and surgery, I

## Bökstedt periodicity and quotients of DVRs, II

Bökstedt periodicity refers to Bökstedt's seminal description of topological Hochschild homology of finite fields. I will discuss a recent project with T. Nikolaus on computations of THH based on a relative version of Bökstedt periodicity. Our main applications are quotients of discrete valuation rings, generalizing Brun’s results for Z/p^n.

## Bökstedt periodicity and quotients of DVRs, I

Bökstedt periodicity refers to Bökstedt's seminal description of topological Hochschild homology of finite fields. I will discuss a recent project with T. Nikolaus on computations of THH based on a relative version of Bökstedt periodicity. Our main applications are quotients of discrete valuation rings, generalizing Brun’s results for Z/p^n.

## Berkovich approach to degenerations of hyper-Kähler varieties

The results are in accordance with the predictions of mirror symmetry, and the recent work about the rational homology of dual complexes of degenerations of hyper-Kähler varieties, due to Kollár, Laza, Saccà and Voisin. This is joint work with Morgan Brown.

## Geometric construction of homology classes in Riemannian manifolds covered by products of hyperbolic planes

We study the homology of Riemannian manifolds of finite volume that are covered by a product of r copies of the hyperbolic plane. Using a variation of a method developed by Avramidi and Nyguen-Phan, we show that any such manifold M possesses, up to finite coverings, an arbitrarily large number of compact oriented flat totally geodesic r-dimensional submanifolds whose fundamental classes are linearly independent in the r-th homology group of M.

## The maximum of the Riemann zeta function on the 1-line

We consider upper bounds of the Riemann zeta function on the 1-line and demonstrate a link with the maximum of the function S(t) - the remainder in the formula for the number of non-trivial zeros of height t in the critical strip. In particular, we show that a conjecture of Littlewood on the maximum of \zeta(1+it) follows from a folklore conjecture on the max of S(t).

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## Talk coaching for Postdocs

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## Homotopy Algebras III: Examples and Applications

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