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Autumn Semester 2021

Date / Time Speaker Title Location
28 September 2021
16:30-17:30 		Dr. Kaloyan Slavov
ETHZ
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Zurich Graduate Colloquium

Title What is... Chebotarev density?
Speaker, Affiliation Dr. Kaloyan Slavov, ETHZ
Date, Time 28 September 2021, 16:30-17:30
Location KO2 F 150
Abstract Take a polynomial map \(\mathbb{F}_q\to\mathbb{F}_q\) over a (large) finite field and compute the fraction of elements in its image. Most likely, you got \(\approx 0.632\). Once we explain why that is, we arrive at a group theory question: Suppose a subgroup $G$ of the symmetric group \(S_n\) has the same fraction of fixed-point-free elements as \(S_n\) itself. Does it follow that \(G=S_n$\)? The talk will be nontechnical. We will invoke a property of \(e=2.71...\).
What is... Chebotarev density?read_more
KO2 F 150
19 October 2021
16:30-17:30 		Raphael Schumacher
ETHZ
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Zurich Graduate Colloquium

Title What is... an automorphic form on GL(3,R)?
Speaker, Affiliation Raphael Schumacher, ETHZ
Date, Time 19 October 2021, 16:30-17:30
Location KO2 F 150
Abstract Around 1980, Jacquet, Piatetski-Shapiro and Shalika published their paper "Automorphic Forms on \(\mathrm{GL}(3)\)" and Bump his book "Automorphic Forms on \(\mathrm{GL}(3,\mathbb{R})\)" in which they founded the theory of automorphic forms on \(\mathrm{GL}(3)\) and proved the functional equation for an \(L\)-function attached to an automorphic representation of \(\mathrm{GL}_3(\mathbb{A})\) for the first time.
As in these two works, we will introduce Hecke-Maass cusp forms \(\phi\in\pi\) on \(\mathrm{GL}(3)\), their first projections \(\phi^1\) and their Fourier-Whittaker expansions. To do this, we have to define the corresponding Whittaker functions \(W_\phi\), the related dual automorphic forms \( ilde{?}\) and their dual Whittaker functions \(\widetilde{W}_\phi\). We will also have to prove some properties of the Fourier- Whittaker coefficients of Hecke-Maass cusp forms on \(\mathrm{GL}(3)\).
In the end of our talk, we will discuss the various functional equations related to the \(L\)-function on \(\mathrm{GL}(3)\) coming from an arbitrary Hecke-Maass cusp form \(\phi\in\pi\). This is done without the limitation of \(L\)-functions coming only from Maass forms as in Bump's book.
What is... an automorphic form on GL(3,R)?read_more
KO2 F 150
2 November 2021
16:30-17:30 		Alessandro Lägeler
ETHZ
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Zurich Graduate Colloquium

Title What is... a Dedekind sum?
Speaker, Affiliation Alessandro Lägeler, ETHZ
Date, Time 2 November 2021, 16:30-17:30
Location KO2 F 150
Abstract Dedekind Sums first arose in the 19th century as correction terms of the transformation of the logarithm of a certain modular form. However, they are finite elementary sums and appear in a wide range of subjects as geometry, topology, computer science, and mathematical physics. In this talk, we will go the other way around: We start with a selection of examples of applications without any reference to modular forms. Towards the end, we discuss their connection to the Dedekind eta-function.
What is... a Dedekind sum?read_more
KO2 F 150
9 November 2021
16:30-17:30 		Dr. Maxim Mornev
EPFL
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Zurich Graduate Colloquium

Title What is... a shtuka?
Speaker, Affiliation Dr. Maxim Mornev, EPFL
Date, Time 9 November 2021, 16:30-17:30
Location KO2 F 150
Abstract In the literature there are many seemingly incompatible definitions of a shtuka. I will explain the unifying idea which stands behind them. I will also discuss applications of shtukas to Langlands program and to the theory of Galois representations.
What is... a shtuka?read_more
KO2 F 150
16 November 2021
16:30-17:30 		Paula Truöl
ETHZ
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Zurich Graduate Colloquium

Title What is... a slice knot?
Speaker, Affiliation Paula Truöl, ETHZ
Date, Time 16 November 2021, 16:30-17:30
Location KO2 F 150
Abstract Knot theory is a subarea of low-dimensional topology - the study of smooth manifolds of dimension 4 or less. Classical knots are smooth embeddings of the (oriented) circle S^1 into R^3 (or into the 3-sphere), usually studied up to an equivalence relation called ambient isotopy. The concept of "sliceness" is a (natural) generalization in dimension 4 of the question whether certain knots are isotopic to the trivial knot (the so-called unknot). In the talk, we will define all the relevant terms and give examples of slice knots. Along the way, we will see some related important results from low-dimensional topology. For example, the study of slice knots is connected to the existence of "exotic" smooth structures on R^4.
What is... a slice knot?read_more
KO2 F 150
30 November 2021
16:30-17:30 		Giada Franz
ETHZ
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Zurich Graduate Colloquium

Title What is... a minimal surface?
Speaker, Affiliation Giada Franz, ETHZ
Date, Time 30 November 2021, 16:30-17:30
Location KO2 F 150
Abstract Minimal surfaces are very natural objects to consider since they are surfaces that minimize the area, globally or just locally.
This talk is meant to be a general introduction to these objects in different settings and an overview of some interesting questions and results, mainly related to the problem of the existence of minimal surfaces.
What is... a minimal surface?read_more
KO2 F 150
7 December 2021
16:30-17:30 		Dr. Elif Saçikara
UZH
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Zurich Graduate Colloquium

Title What is... a q-matroid?
Speaker, Affiliation Dr. Elif Saçikara, UZH
Date, Time 7 December 2021, 16:30-17:30
Location KO2 F 150
Abstract In combinatorics, a q-analog of a discrete structure is defined by replacing finite sets with finite dimensional vector spaces. In this talk, we consider this notion over a specific structure, matroids. After presenting certain equivalent axiomatic definitions of a matroid, we discuss their q-analogs by comparing differences and similarities with the classical case. Finally, as a construction and an application of a q-matroid, we mention their relation with a q-analog of other combinatorial objects called designs, and state some open questions.
What is... a q-matroid?read_more
KO2 F 150
21 December 2021
16:30-17:30 		Manuel Tecchiolli
UZH
Details

Zurich Graduate Colloquium

Title What is... time?
Speaker, Affiliation Manuel Tecchiolli, UZH
Date, Time 21 December 2021, 16:30-17:30
Location KO2 F 150
Abstract This talk is an introduction to the philosophy of time. We will discuss the main ideas behind the modern conceptions of time and give the basic, although necessary, knowledge in order to be able to understand the principal theories of time that the philosophical literature offers: A- and B-frameworks, the meaning of change and McTaggart's paradox, relativistic McTaggart's paradox and the unreality of time, asymmetries within time and the common idea of entropy as an arrow of time.
What is... time?read_more
KO2 F 150

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