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Title: Rationality Problems 1
Hashtag: #workshop
Title: Measures of Irrationality
Hashtag: #workshop
Title: Cremona 1
Hashtag: #workshop
Title: Eigenvalues for the random-to-below shuffle
Speaker: Nadia Lafrenière [Dartmouth College]
Abstract: The random-to-below shuffle of a deck of cards consists of removing any
card at random (with uniform probability), and inserting it anywhere
below (with uniform probability). A surprising fact is that the
eigenvalues of its transition matrix are all rational and positive. This
is unexpected for a non-symmetric matrix, and suggests some
combinatorial interpretation. I’ll discuss an expression of the
eigenvalues in terms of lacunar sets, namely sets with no consecutive
integers, and make connections with the well studied top-to-random
shuffle. I'll then suggest how this may be extended to standard
tableaux. I’ll finally describe a more straightforward way to compute a
stopping time for this shuffle, answering the question of how long we
would need to shuffle to get a well-mixed deck using this shuffling
technique.
This is joint work with Darij Grinberg.
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Title: Curves in Varieties 1
Hashtag: #workshop
Title: Speed Talks
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Title: Rationalities Problems 2
Hashtag: #workshop
Title: Measure of Irrationality 2
Hashtag: #workshop
Title: Cremona 2
Hashtag: #workshop
Title: Curves in Varieties
Hashtag: #workshop
Title: Rationality Problems 3
Hashtag: #workshop
Title: Measures of Irrationality 3
Hashtag: #workshop
Title: Cremona 3
Hashtag: #workshop
Title: What is the group of a quantum group?
Speaker: Frank Verstraete [Cambridge Univ.]
Abstract: We discuss the categorical description of quantum group symmetries, with applications to quantum spin chains. In particular, we review how representations of quantum groups SU(2)_q can be used to construct nontrivial representations of the SU(2) symmetries of the XXZ spin chain. The main technical tools used in this work are tensor networks and matrix product operator symmetries, see e.g. https://arxiv.org/abs/2008.11187.
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Title: TBA
Speaker: Alena Erchenko [Dartmouth College]
Abstract: TBA
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Title: Measures of Irrationality 4
Hashtag: #workshop
Title: Curves in Varieties 3
Hashtag: #workshop
Hashtag: #workshop
Title: Cremona 4
Hashtag: #workshop
Title: Curves in Variety 4
Hashtag: #workshop
Title: Regular and stochastic properties of the maximal entropy measure on CP(k), k=1,2.
Speaker: Christophe Dupont [Universite de Rennes 1]
Abstract: A rational map of degree d > 1 on CP(1) has a unique measure of maximal entropy mu. Its Lyapunov exponent lambda is bounded below by (1/2) log d and its dimension m is equal to log d / lambda. Moreover, mu is absolutely continuous with respect to the m-Hausdorff measure if and only if f is a power, Tchebichev or Lattès map. This rigidity result, due to Zdunik, relies on stochastic properties for mu, provided by the convergence of a geometric coding tree, worked out by Przytycki-Urbanski-Zdunik. In this talk, we shall review counterpart results for holomorphic mappings on CP(2) (which are no more conformal) and discuss open problems in this context.
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