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Autumn Semester 2019

Date / Time Speaker Title Location
24 September 2019
17:15-18:30 		Andres Fontalvo Orozco
Universität Zürich
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Zurich Graduate Colloquium

Title What is... an m-trace?
Speaker, Affiliation Andres Fontalvo Orozco, Universität Zürich
Date, Time 24 September 2019, 17:15-18:30
Location KO2 F 150
Abstract An m-trace is a generalization of the concept of the trace of a matrix. In this talk I will first introduce the categorical trace, and review some of its interesting properties and some of the problems that arise when used in a non semisimple setting. Finally, I will introduce the m-trace as a way to fix these issues.
What is... an m-trace?read_more
KO2 F 150
1 October 2019
17:15-18:30 		Gianira Nicoletta Alfarano
Universität Zürich
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Zurich Graduate Colloquium

Title What is... a convolutional code?
Speaker, Affiliation Gianira Nicoletta Alfarano, Universität Zürich
Date, Time 1 October 2019, 17:15-18:30
Location KO2 F 150
Abstract The theory of error-correcting codes has inspired many mathematicians who were interested in applying techniques from algebra and discrete mathematics in order to progress on questions in information processing. Convolutional codes were introduced in 1955 by Peter Elias, as an interesting natural generalization of classical block codes and they have been widely implemented in practice with applications in mobile communications, satellite communications and data streaming. In this talk, we are going to introduce the theory of error-correcting codes and the classical theory of linear block codes. Then, we will give a mathematical description of convolutional codes, by using module theory over a polynomial ring and we will discuss their most important parameters.
What is... a convolutional code?read_more
KO2 F 150
8 October 2019
17:15-18:30 		Merlin Incerti-Medici
Universität Zürich
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Zurich Graduate Colloquium

Title What are... points at infinity?
Speaker, Affiliation Merlin Incerti-Medici, Universität Zürich
Date, Time 8 October 2019, 17:15-18:30
Location KO2 F 150
Abstract Ever since the discovery of the hyperbolic plane, negatively curved spaces have been studied from many different points of view and have served to connect different areas of mathematics. One object that has been particularly useful in this endeavour is the boundary at infinity, which consists of all 'directions' in which one can walk to infinity. We will introduce the boundary at infinity, define several basic tools to work with it and illustrate its uses.
What are... points at infinity?read_more
KO2 F 150
15 October 2019
17:15-18:30 		Dr. Jagna Wisniewska
ETHZ
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Zurich Graduate Colloquium

Title Whats is... a tentacular Hamiltonian?
Speaker, Affiliation Dr. Jagna Wisniewska, ETHZ
Date, Time 15 October 2019, 17:15-18:30
Location KO2 F 150
Abstract Hamiltonian mechanics originates from physics, more precisely from classical mechanics. Examples of such systems can be found in celestial mechanics, describing the motion of a satellite under the gravitational forces of several astronomical objects. One of the main questions in Hamiltonian mechanics is to find periodic orbits on a fixed energy level set. In my talk, I will introduce the notion of Rabinowitz Floer homology and show how this algebraic invariant can be applied to the special class of tentacular Hamiltonians to answer the question of existence of periodic orbits for Hamiltonian systems on a fixed, non-compact energy levels.
Whats is... a tentacular Hamiltonian?read_more
KO2 F 150
26 November 2019
17:15-18:30 		Raúl Penaguião
Universität Zürich
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Zurich Graduate Colloquium

Title What is... a combinatorial presheaf?
Speaker, Affiliation Raúl Penaguião, Universität Zürich
Date, Time 26 November 2019, 17:15-18:30
Location KO2 F 150
Abstract The study of substructures in combinatorics is seminal in mathematics: a striking example is the characterization of planar graphs through its description of minors due to Kuratowski. Lately there has been a new construction of a Hopf algebra from patterns in permutations: that is, an algebraic object that is ideal to encode the notion of merging and splitting. We start our journey to encode substructures of permutations in a categorical way through combinatorial presheaves, that will bring us from category theory to factorization trees. Finally, we observe that the pattern Hopf algebra construction for permutations is not really restricted to permutations, but to any combinatorial object that allows for substructures.
What is... a combinatorial presheaf?read_more
KO2 F 150
3 December 2019
17:15-18:30 		Emilio Corso
ETHZ
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Zurich Graduate Colloquium

Title What is... measure rigidity?
Speaker, Affiliation Emilio Corso, ETHZ
Date, Time 3 December 2019, 17:15-18:30
Location KO2 F 150
Abstract In an influential paper published in 1967, Furstenberg marked the outset of the study of rigidity properties for invariant measures arising in algebraically-defined dynamical systems. His conjectures and achievements prompted intensive research activity, purporting to understand the manifestation of similar rigidity phenomena in ever more general contexts. Recent developments along this line of investigation turned out to be paramount for the (complete or partial) resolution of long-standing conjectures pertaining to Hilbert's eleventh problem, Diophantine approximation, equidistribution of Hecke-Maass forms and the kinematics of high-energy quantum particles, statistical properties of the Lorentz gas with quasicrystal scatterer configurations. I will survey some of these applications, hopefully shedding some light on how measure rigidity comes into play.
What is... measure rigidity?read_more
KO2 F 150
10 December 2019
17:15-18:30 		Roland Prohaska
ETH Zürich
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Zurich Graduate Colloquium

Title What is... a badly approximable number?
Speaker, Affiliation Roland Prohaska, ETH Zürich
Date, Time 10 December 2019, 17:15-18:30
Location KO2 F 150
Abstract Badly approximable numbers are irrational numbers whose rational approximations are, in some sense, as inefficient as possible. We will define them, give a survey of their basic properties, and present a dynamical characterization in terms of the geodesic flow on the space of unimodular lattices in the plane. Known as the Dani correspondence principle, this connection has recently been used to answer a good number of long-standing questions about badly approximable numbers, such as their prevalence on certain fractal sets.
What is... a badly approximable number?read_more
KO2 F 150

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