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MAT070
Zurich Colloquium in Mathematics
Zeiten:
Di 16.30 - 18.00 Raum: KO2F150 Plätze:
Organisiert von
Prof. Dr. Joseph Ayoub, Prof. Dr. Afonso Bandeira, Prof. Dr. Mikaela Iacobelli, Prof. Dr. Alessandra Iozzi, Prof. Dr. Siddhartha Mishra, Prof. Dr. Rahul Pandharipande, Prof. Dr. Stefan Sauter, Prof. Dr. Benjamin Schlein
Talks
23.09.2025
An exponential improvement for diagonal Ramsey
The Ramsey number R(k) is the minimum n such that every red-blue colouring of the edges of the complete graph on n vertices contains a monochromatic copy of K_k. It has been known since the work of Erdos and Szekeres in 1935, and Erdos in 1947, that 2^{k/2} < R(k) < 4^k, but until recently the only improvements were by lower order terms. In this talk I will give an introduction to the area, and also sketch the proof of a recent result, which improves the upper bound of Erdos and Szekeres by a (small) exponential factor. Based on joint work with Marcelo Campos, Simon Griffiths and Julian Sahasrabudhe.
The Ramsey number R(k) is the minimum n such that every red-blue colouring of the edges of the complete graph on n vertices contains a monochromatic copy of K_k. It has been known since the work of Erdos and Szekeres in 1935, and Erdos in 1947, that 2^{k/2} < R(k) < 4^k, but until recently the only improvements were by lower order terms. In this talk I will give an introduction to the area, and also sketch the proof of a recent result, which improves the upper bound of Erdos and Szekeres by a (small) exponential factor. Based on joint work with Marcelo Campos, Simon Griffiths and Julian Sahasrabudhe.
Rob Morris
IMPA
IMPA
30.09.2025
Vanishing negative K-theory and bounded t-structures
We will begin with a quick reminder of algebraic K-theory, and a few classical, vanishing results for negative K-theory. The talk will then focus on a striking 2019 article by Antieau, Gepner and Heller - it turns out that there are K-theoretic obstructions to the existence of bounded t-structures. The result suggests many questions. A few have already been answered, but many remain open. We will concentrate on the many possible directions for future research.
We will begin with a quick reminder of algebraic K-theory, and a few classical, vanishing results for negative K-theory. The talk will then focus on a striking 2019 article by Antieau, Gepner and Heller - it turns out that there are K-theoretic obstructions to the existence of bounded t-structures. The result suggests many questions. A few have already been answered, but many remain open. We will concentrate on the many possible directions for future research.
Amnon Neeman
The Australian National University
The Australian National University
14.10.2025
Kakeya sets in R^3
A Kakeya set is a compact subset of R^n that contains a unit line segment pointing in every direction. Kakeya set conjecture asserts that every Kakeya set has Minkowski and Hausdorff dimension n. We prove this conjecture in R^3 as a consequence of a more general statement about union of tubes. This is joint work with Josh Zahl.
A Kakeya set is a compact subset of R^n that contains a unit line segment pointing in every direction. Kakeya set conjecture asserts that every Kakeya set has Minkowski and Hausdorff dimension n. We prove this conjecture in R^3 as a consequence of a more general statement about union of tubes. This is joint work with Josh Zahl.
Hong Wang
Institut des Hautes Études Scientifiques
Institut des Hautes Études Scientifiques