Alternatively have a look at the program.

## Euler characteristics and 4-manifolds

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

We consider the Euler characteristics of closed orientable 2n-manifolds with a given fundamental group G, and highly-connected universal cover. We strengthen the 4-dimensional Hausmann-Weinberger estimates and extend to higher dimensions. As an application we obtain new restrictions for non-abelian finite groups arising as fundamental groups of rational homology 4-spheres.

## Invariance of Knot Lattice Homotopy

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

## tba -- CANCELLED --

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

## A New Gauge-Theoretic Construction of 4-Dimensional Hyperkähler ALE Spaces

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

## Strongly quasipositive knots are concordant to infinitely many strongly quasipositive knots

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

## The Nielsen realization for non-spin 4-manifolds

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

## 4-genus bounds from the 10/8+4 theorem

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

Donald and Vafaee described a way to use Furuta’s 10/8 theorem to obstruct sliceness in the 4-ball and Linh Truong used a refinement, the 10/8 +4 theorem of Hopkins-Lin-Shi and Hu, to strengthen this sliceness obstruction. We will show how to expand on this technique to obtain lower bounds for four-ball genus and present some calculations for satellite knots. This is joint work in progress with Sashka Kjuchukova and Linh Truong.

## SU(2) representations of small Dehn surgeries on knots

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

## Squeezed knots

(Joint work with Peter Feller and Lukas Lewark). A knot is called squeezed if it is a slice of a minimal genus, oriented, connected cobordism from a positive to a negative torus knot. Many popular classes of knots are squeezed. At most six knots of ten or fewer crossings are not squeezed. The Lipshitz-Sarkar stable homotopy type for Khovanov homology provides a (surprisingly?) effective means of obstructing knots from being squeezed. I'll explain all this and also advertize a cash prize of 271 swiss francs.

## Geometry, topology, and effective rigidity of hyperbolic 3-manifolds

Contact: Aru Ray

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