François Charles, Université Paris-Sud (Orsay)
Constructing curves on surfaces
Giovedì 06 Ottobre 2016, ore 16:30
Sala di rappresentanza, Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50 | |
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Endre Szemerédi, Rutgers University
On the fundamental theorem of Freiman
Lunedì 03 Ottobre 2016, ore 16:03
Aula Chisini, via Saldini 50 | |
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Walter Craig, McMaster University
Vortex filament dynamics
Mercoledì 21 Settembre 2016, ore 16:30 precise
Sala di rappresentanza, Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50 | |
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Elon Lindenstrauss, Hebrew University of Jerusalem
DIAGONAL FLOWS, JOININGS AND ARITHMETIC
Lunedì 11 Luglio 2016, ore 16:30
Aula Chisini, via Saldini 50 | |
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ALEX LUBOTSKY, Hebrew University and ETH-Zurich
COLLOQUIUM DIPARTIMENTO DI MATEMATICA E APPLICAZIONI, MILANO-BICOCCA con SEMINARIO MATEMATICO E FISICO DI MILANO: "High dimensional expanders: from Ramanujan graphs to Ramanujan complexes"
Giovedì 12 Maggio 2016, ore 15:30
Aula 3014, edificio U5 del Dipartimento di Matematica e Applicazioni, Universita' di Milano - Bicocca, Via R. Cozzi 55 |
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Abstract
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Expander graphs in general, and Ramanujan graphs, in particular, have played a major role in combinatorics and computer science in the last 4 decades and more recently also in pure math. Approximately 10 years ago a theory of Ramanujan complexes was developed by Li, Lubotzky-Samuels-Vishne and others.
In recent years a high dimensional theory of expanders is emerging. The notions of geometric and topological expanders were defined by Gromov in 2010 who proved that the complete d-dimensional simplicial complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. Ramanujan complexes were shown to be geometric expanders by Fox-Gromov-Lafforgue-Naor-Pach in 2013, but it was left open if they are also topological expanders.
By developing new isoperimetric methods for "locally minimal small" F_2- co-chains, it was shown recently by Kaufman- Kazdhan- Lubotzky for small dimensions and Evra-Kaufman for all dimensions that the d-skeletons of (d+1)-dimensional Ramanujan complexes provide bounded degree topological expanders. This answers Gromov's original problem, but still leaves open whether the Ramanujan complexes themselves are topological expanders.
it was shown recently by Kaufman- Kazdhan- Lubotzky for small dimensions and Evra-Kaufman for all dimensions that the d-skeletons of (d+1)-dimensional Ramanujan complexes provide bounded degree topological expanders. This answers Gromov's original problem, but still leaves open whether the Ramanujan complexes themselves are topological expanders.
We will describe these developments and the general area of high dimensional expanders and some of its open problems. |
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Alessandro Giuliani, Università di Roma 3
Height fluctuations and universality relations in interacting dimer models
Mercoledì 04 Maggio 2016, ore 16:00
Sala di rappresentanza, Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50 | |
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