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Autumn Semester 2024

Date / Time Speaker Title Location
17 September 2024
16:30-17:30 		Robert Nowak
Universität Ulm
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Zurich Graduate Colloquium

Title What is... the arithmetic of curves and semistable reduction?
Speaker, Affiliation Robert Nowak, Universität Ulm
Date, Time 17 September 2024, 16:30-17:30
Location KO2 F 150
Abstract Let Y be an algebraic curve over a number field K of genus at least 1. The reduction behavior of Y to characteristic p>0 can be used to compute arithmetic invariants of the curve. In this talk we will introduce notions of good, bad, and semistable reduction and discuss their connection to the L-series and the conductor of the curve. In the special case of hyperelliptic curves and p = 2, we will study the minimal extension over which the curve attains semistable reduction and the automorphism groups of the special fiber.
What is... the arithmetic of curves and semistable reduction?read_more
KO2 F 150
29 October 2024
16:30-17:30 		Beatrice Toesca di Castellazzo
Universität Zürich
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Zurich Graduate Colloquium

Title What is... Network Coding?
Speaker, Affiliation Beatrice Toesca di Castellazzo, Universität Zürich
Date, Time 29 October 2024, 16:30-17:30
Location KO2 F 150
Abstract Suppose you want to send a message to your friend. Can errors occur during the transmission? Unfortunately yes. It is then crucial to find ways to detect errors in the received message and possibly correct it. The goal of algebraic coding theory is to design ways of encoding messages (vectors over a finite field) with an algebraic structure that guarantees that, with a limited number of errors, the meaning of the original message is not compromised. In multi-cast communication, as in the streaming of data over the Internet, one deals with sending information to multiple receivers across a network with several intermediate nodes. To improve the network throughput, a coding technique called random linear network coding was developed. In this scenario, the intermediate nodes transmit a random linear combination of the vectors received. With this technique, it is possible to asymptotically achieve the maximum capacity of the network, without relying on its topology. In this talk, we will start studying the basic notions of coding theory with only one sender and one receiver, and then switch to the case of data transmission over a network and explain how in this case giving the messages the structure of a linear subspace helps correcting errors.
What is... Network Coding?read_more
KO2 F 150
5 November 2024
16:30-17:30 		Jeremy Feusi
ETH
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Zurich Graduate Colloquium

Title What is... log geometry?
Speaker, Affiliation Jeremy Feusi, ETH
Date, Time 5 November 2024, 16:30-17:30
Location KO2 F 150
What is... log geometry?
KO2 F 150
12 November 2024
16:30-17:30 		Andrea Ulliana
Universität Zürich
Details

Zurich Graduate Colloquium

Title What is... Szemerédi's Theorem?
Speaker, Affiliation Andrea Ulliana, Universität Zürich
Date, Time 12 November 2024, 16:30-17:30
Location KO2 F 150
Abstract As firstly conjectured by Erdös and Turán in 1936, in 1972 Szemerédi proved that any positive density subset of \(N\) contains arbitrary long arithmetic progressions. Determinant contributions came from very different fields: harmonic analysis, graph theory and ergodic theory. This theorem uncovered deep connections between these fields and sits at the foundation of the celebrated Green-Tao theorem about arithmetic progressions of prime numbers. During the talk we will introduce the notion of density of a subset of \(N\) and we will motivate the statement of the theorem. We will then turn our attention to Roth's theorem (Szemerédi's theorem for arithmetic progressions of length 3): we will sketch the harmonic analysis proof by Roth (1953) and we will mention Szemerédi's alternative one, that exploits the 'subgraph removal lemma' and opened the way to a proof of Szemerédi's theorem. Finally we will discuss Furstenberg alternative proof (1977) of Szemerédi's theorem, based on his 'Correspondence principle' between subsets of \(N\) and measure preserving dynamical systems.
What is... Szemerédi's Theorem?read_more
KO2 F 150
19 November 2024
16:30-17:30 		Catalina-Andreea Jurja
Universität Zürich
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Zurich Graduate Colloquium

Title What is... fluid dynamics?
Speaker, Affiliation Catalina-Andreea Jurja, Universität Zürich
Date, Time 19 November 2024, 16:30-17:30
Location KO2 F 150
Abstract A mathematically rigorous description of fluid motion plays an important role, for example in understanding weather patterns or ocean dynamics. In this talk, we will derive the fundamentals equations of motions for an inviscid incompressible fluid -- the Euler equations. We will present known results as well as related open problems. Finally, we will discuss stability for 2D stratified flows relevant in geophysics.
What is... fluid dynamics?read_more
KO2 F 150
3 December 2024
16:30-17:30 		Annika Weidmann
ETH
Details

Zurich Graduate Colloquium

Title What is... a pseudo-finite field?
Speaker, Affiliation Annika Weidmann, ETH
Date, Time 3 December 2024, 16:30-17:30
Location KO2 F 150
What is... a pseudo-finite field?
KO2 F 150
10 December 2024
16:30-17:30 		Lycka Drakengren
ETH
Details

Zurich Graduate Colloquium

Title What is... the torelli map?
Speaker, Affiliation Lycka Drakengren, ETH
Date, Time 10 December 2024, 16:30-17:30
Location KO2 F 150
What is... the torelli map?
KO2 F 150
17 December 2024
16:30-17:30 		Ludovica Buelli
University of Genoa
Details

Zurich Graduate Colloquium

Title What is... Hyperkähler Geometry?
Speaker, Affiliation Ludovica Buelli, University of Genoa
Date, Time 17 December 2024, 16:30-17:30
Location KO2 F 150
Abstract manifolds, both from a complex analytic and algebraic point of view. This kind of manifolds plays a central role in classification problems in complex algebraic geometry, being fundamental building blocks of Ricci-flat manifolds, and their theory has become a very popular research topic in the last years. Together with their definition(s) and their main properties, we will see the four known families of deformation classes of this kind of manifolds and we will approach the problem of their bimeromorphic classification.
What is... Hyperkähler Geometry?read_more
KO2 F 150

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