Přednášky se konají v období 31.3. - 3.4.2025, v budově ÚMS (M4, M5 a zasedací místnost, 2. patro)

Jonathan Kirby

Model Theory, Exponentiation and Quasiminimality

Po 31.3. 14:00 - 15:00 (zasedací místnost, 2. patro)
Út 1.4. 11:00 - 12:00 (M4)
St 2.4. 14:00 - 15:00 (M5)
Čt 3.4. 10:00 - 11:00 (zasedací místnost, 2. patro)

Abstract: Model Theory is a way of looking at mathematical concepts which is sensitive to the choice of language we use to describe them. One of its achievements is to classify different mathematical theories according to their complexity. In this series of talks I will survey some of the work done towards understanding the model theory of exponential fields, including the real exponential and Zilber’s approach to the complex exponential field. We know from Wilkie that the real exponential field is not too complicated (it is o-minimal) and this has good consequences in geometry, in number theory, and even in machine learning. For the complex exponential, we do not know if it is tame (quasiminimal) or whether it is maximally complicated (interpreting both reals and integers). I will explain progress towards proving that it is tame.

Mathematics, Physics & Computer Science Seminar Series

Seminář se koná 26.3.2025 od 16:30 v zasedací místnosti 200, Komenského náměstí 220/2

EVA MIRANDA

Certainty in UncertainTimes – From Hilbert’s Dream to Chaos

Will the 2024 YR4 asteroid strike Earth? Science’s answer: maybe. With a  shifting probability, it could arrive dramatically on Christmas Eve 2032. Despite our reliance on mathematics and physics for precise predictions, history warns us that certainty is elusive.
David Hilbert once dreamed of a world where reason would conquer uncertainty, but Alan Turing shattered this vision with his proof of the undecidability of the halting problem. Chaos theory warns that even minor measurement errors can escalate into vast unpredictability. Celestial mechanics, once seen as deterministic, reveals a universe more chaotic than Newton had imagined.
Beyond classical chaos lies a deeper enigma—logical chaos. In 2021, collaborating with Robert Cardona, Daniel Peralta-Salas, and Francisco Presas, I demonstrated the existence of undecidable fluid paths—trajectories so complex that no logical framework can predict their evolution. Could similar undecidable phenomena exist in celestial mechanics? Are there cosmic events so complex that no theory, no supercomputer will ever decipher them?

Další informace ZDE.