dating back to the foundational paper by john von neumann, a fundamental theme in ergodic theory is the \emph{isomorphism problem} to classify invertible measure-preserving transformations (mpt's) up to isomorphism. in a series of papers, matthew foreman, daniel rudolph and benjamin weiss have shown in a rigorous way that such a classification is impossible. besides isomorphism, kakutani equivalence is the best known and most natural equivalence relation on ergodic mpt's for which the classification problem can be considered. in joint work with marlies gerber we prove that the kakutani equivalence relation of ergodic mpt's is not a borel set. this shows in a precise way that the problem of classifying such transformations up to kakutani equivalence is also intractable.

in this talk, we study the property of the solution of semidefinite programs with multi-dimensional perturbation variables using the davidenko di erential equations. under the assumptions of strict complementary and non-degeneracy, we aim to find the a priori unknown maximal convex permissible perturbation set where the semidefinite program has a unique optimum and the optimum is analytic. a sweeping euler numerical method is developed to approximate this a priori unknown perturbation set and solve the semidefinite program within this set. we prove local and global error bounds for this second-order sweeping euler scheme and demonstrate results on several examples.

a central sequence in a $c^*$-algebra is a sequence (x\_n) of elements such that [x\_n, a] converges to zero, for any element a of the $c^*$-algebra. in von neumann algebra setting one typically means the convergence with respect to tracial norms, while in $c^*$-theory it is with respect to the $c^*$-norm. in this talk we will consider the $c^*$-theory version of central sequences. we will discuss properties of central sequence algebras and in particular address a question of j. phillips and of ando and kirchberg of which separable $c^*$-algebras have abelian central sequence algebras.
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joint work with dominic enders.

a central problem in low-dimensional topology asks which homology 3-spheres bound contractible 4-manifolds and homology 4-balls. in this talk, we address this problem for plumbed 3-manifolds and we
present the classical and new results together. our approach is based on
mazur’s famous argument which provides a unification of all results in a
fairly simple way.

the thin obstacle problem is a classical free boundary problem arising from the study of an elastic membrane resting on a lower-dimensional obstacle. concerning the behavior of the solution near a contact point between the membrane and the obstacle, many important questions remain open. in this talk, we discuss a unified method that leads to a rate of convergence to `tangent cones' at contact points with integer frequencies.
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this talk is based on a recent joint work with ovidiu savin.

metric algebraic geometry is a term proposed for the study of properties of real algebraic varieties that depend on a distance metric. the distance metric can be the euclidean metric in the ambient space or a metric intrinsic to the variety. in this talk, we introduce metric algebraic geometry through a discussion of voronoi cells, bottlenecks, offset hypersurfaces, and the reach of an algebraic variety. we also show applications to the computational study of the geometry of data with nonlinear models.

let $\pi$ be a cuspidal automorphic representation for gl(3) over a
number field. we fix an integer $k \geq 2$ and we assume that the
symmetric $m$th power lifts of $\pi$ are automorphic for $m \leq k$,
cuspidal for $m < k$, and that certain associated rankin–selberg
products are automorphic. in this setting, we bound the number of
cuspidal isobaric summands in the $k$th symmetric power lift. in
particular, we show it is bounded above by 3 for $k \geq 7$, and bounded
above by 2 when $k \geq 19$ with $k$ congruent to 1 mod 3. we will also
discuss the analogous problem for gl(4).

the talk will be an overview of comparison methods for stochastic models and risks by muller and stoyan, and stochastic orderings for markov processes on partially ordered sets, by william massey.

let $x$ be a smooth projective variety whose algebra of
holomorphic forms is generated in degree at most $2$, for instance an
abelian variety or a hyperk\"ahler manifold. a recent conjecture of voisin