On this page, all Doctoral Students of the *Doctoral Program*
can announce their own talks, presentations, mini-courses etc. To
do so, please fill in the corresponding form.

Link to the doctoral student's page of the academic year 2006/2007, 2007/2008, 2008/2009, 2009/2010, 2010/2011.

Loren Coquille (Geneva) |
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Lecture at the eighth Graduate Colloquium of the Swiss Doctoral Program, Basel 8.9.2011, 11:30: Gibbs measures of the 2d Ising modelAbstract: In the late 1970s, in two celebrated papers, Aizenman and Higuchi independently established that all infinite-volume Gibbs measures of the 2d Ising model are a convex
combination of the two pure phases. After introducing the relevant definitions and concepts needed to understand the physical content of this result, I will present a new
approach to it, with a number of advantages:(i) a finite-volume, quantitative analogue (implying the classical claim) is obtained; (ii) the scheme of the proof seems more natural and provides a better picture of the underlying physical phenomenon; (iii) this new approach seems substantially more robust (possible extension to the Potts model). This is a joint work with Yvan Velenik. |

Matey Mateev (Basel) |
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Lecture at the eighth Graduate Colloquium of the Swiss Doctoral Program, Basel 8.9.2011, 14:00: Hyperplane sections and degree matricesAbstract: If V is a subscheme of P and ^{n}F is a general hypersurface of degree d,
then F cuts out on V a subscheme Z = V∩F, which is also a subscheme of F.
A natural and interesting question is to study the properties that either Z or V transfers to the other. In this
talk we will discuss this problem and will show how to construct a curve C in P whose
general hyperplane section ^{3}Z = C∩L in P has a given degree matrix.^{2} |

Aleksandr Kolpakov (Fribourg) |
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Lecture at the eighth Graduate Colloquium of the Swiss Doctoral Program, Basel 8.9.2011, 15:20: Right-angles, hyperbolicity and dimensionAbstract: Right-angled polyhedra turn out to be an interesting family of (almost) hyperbolic polytopes.
They are connected with other various problems and notions, e.g. right-angled
Coxeter groups, Loebell manifolds, combinatorial volume estimates and decompositions of acute-angled polyhedra, dimension bounds. In my talk, a survey on the main part of
this zoo will be given together with a brief explanation of what I'm doing. |

Bastien Marmet (Neuchâtel) |
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Lecture at the eighth Graduate Colloquium of the Swiss Doctoral Program, Basel 8.9.2011, 16:40: Quasi-stationary distributions for stochastic approximation algorithms with constant step size |

Immanuel Stampfli (Basel) |
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Lecture at the eighth Graduate Colloquium of the Swiss Doctoral Program, Basel 9.9.2011, 9:30: On the topologies on ind-varietiesAbstract: In the 1960s Shafarevich introduced ind-varieties in order to explore some naturally occurring groups that allow the structure of an
infinite-dimensional analogon of an algebraic group (such as the group of polynomial automorphisms of ℂ ). Shafarevich defined
an ind-variety as the successive limit of an increasing chain^{n}X_{1} ⊆ X_{2} ⊆ X_{3} ⊆ . . .X, each one closed in the next. There are essentially two ways of endowing
such an ind-variety with a topology. One topology is naturally induced by the increasing
chain of varieties and is due to Shafarevich. The other is naturally induced by the regular
functions on the ind-variety and is due to Kambayashi. These topologies differ on a rather
large class of ind-varieties. The aim of this talk is to give an idea of the proof of this
result. _{n} |

Peter Feller (Bern) |
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Lecture at the eighth Graduate Colloquium of the Swiss Doctoral Program, Basel 9.9.2011, 11:00: Gordian distance, torus knots and three variants of adjacencyAbstract: We define classical knots and explain how they form a discrete metric space with respect
to the Gordian distance. Then we give different descriptions of the subspace of torus
knots. Finally we introduce three notions of adjacency for torus knots and conclude with
some examples of Gordian adjacency and some of our questions. |

Iulian Ion Simion (EPFL) |
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Lecture at the eighth Graduate Colloquium of the Swiss Doctoral Program, Basel 9.9.2011, 13:30: Witt groups in linear algebraic groupsAbstract: After a description of Witt groups I will show how they play a role in my current work
namely in studying the centralizer of unipotent elements in linear algebraic groups for
small characteristic. We will describe how one constructs such subgroups with examples
both in the classical and exceptional cases. |

Maike Massierer (Basel) |
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Lecture at the eighth Graduate Colloquium of the Swiss Doctoral Program, Basel 9.9.2011, 11:30: Trace zero varieties in cryptographyAbstract: Elliptic curves defined over finite fields are one of the most important types of groups used
in cryptography today. Trace zero varieties arise from certain subgroups of such elliptic
curves, namely those points of trace zero. They are interesting from a constructive point
of view, because they allow fast arithmetic, and also from a cryptanalytic point of view,
since the security of many cryptographic protocols is directly linked to the properties
of these varieties. For both constructive and destructive use of trace zero varieties, it is
important to be able to efficiently represent their elements. We discuss the geometric
construction that leads to the trace zero variety, and how to find an easy and compact
representation of trace zero elements. |