Tentative programme of the DIAMANT/EIDMA symposium, 27-28 May 2010


Thursday
 
10:30-10:55
arrival and coffee
10:55-11:00
opening
Mirjam Dür
Copositive Optimization
11:00-11:55
Copositive optimization can be seen as a generalization of semidefinite programming, since it means optimizing over the cone of so called copositive matrices. A matrix is called copositive if its quadratic form takes nonnegative values on the nonnegative orthant. Obviously, every positive semidefinite matrix is copositive, and so is every entrywise nonnegative matrix, but the copositive cone is significantly larger than both the semidefinite and the nonnegative matrix cones.
Similar to SDP, copositive programs play a role in combinatorial and quadratic optimization. In contrast to SDP, however, in many cases copositive programs provide exact reformulations rather than relaxations. This fact has led to new approaches to combinatorial problems like max clique, QAP, graph partitioning, and graph coloring problems, as well as to certain nonconvex quadratic problems.
The talk will give an introduction to this rather young field of research. We will discuss properties of the copositive cone and its dual, the so called completely positive cone. We will give an overview on problem classes that can be treated as copositive problems, and discuss various solution approaches to solve copositive programs.
Shoumin Liu Brauer algebras of type C
12:00-12:25
For each n>1, we define an algebra that has many properties that one may expect to hold for a Brauer algebra of type Cn. The monomials of this algebra correspond scalar multiples of symmetric Brauer diagrams on 2n strands. Their number is the rank of the algebra.
12:30-13:25 lunch
KP Hart
Algebraic topology but not as you know it
13:30-14:25
Compact Hausdorff spaces have many algebraic aspects. I intend to highlight one of these: a many-valued duality with distributive lattices akin to Stone's duality between compact zero-dimensional spaces and Boolean algebras. The interplay between algebraic properties of the lattices and topological properties of the spaces is very useful in the study of the latter; I will give some examples to illustrate this.
Krzysztof Pietrzak Leakage Resilient Cryptography
14:30-15:10
Traditionally, cryptographers analyze cryptosystems (like encryption or digital signature schemes) as "black-boxes", where a potential adversary can only see the inputs and outputs of the cryptographic algorithm. Unfortunately, in the last decade it became evident that this model does not capture many real world attacks. The reason is that a physical implementation of a cryptosystem (like a smart card) will always leak some additional information during execution, for example its running time or power consumption. Cryptanalytic attacks exploiting such leakage are called "side-channel attacks". Until recently, research on side-channel attacks and countermeasures was mostly done by practitioners. The countermeasures proposed were usually ad-hoc in the sense that they aim at protecting against some particular known attack. This is not very satisfactory, but it was commonly believed that side-channels are a practical problem where theory can only be of limited help. However, many recent results from the theory community suggest that this view was too pessimistic. Cryptosystems were constructed which are provably secure against all (known and unknown) side-channel attacks making some weak (and in some sense minimal) assumptions on the underlying hardware. In this talk I will survey this recent line of research.
15:10-15:25
tea
Christian Eggermont Deadlocks in Open Shop Systems
15:30-15:55
We study algorithmic problems in multi-stage open shop processing systems that are centered around reachability and deadlock detection questions.
Robin de Jong Resultant sequences for division polynomials
 16:00-17:00 Let f be a polynomial with integer coefficients and let (gn) be a sequence of polynomials with integer coefficients, all coprime to f. The sequence of non-zero integers (Res(f,gn)) is called a resultant sequence. One is interested in the relation between analytic properties of such sequences (such as growth behavior) on the one hand and arithmetic properties on the other (such as whether new prime factors will keep occurring, and how often). Traditional cases are the cases where the gn are the polynomials Xn - 1 (a long story going back to Lucas, Pierce, Lehmer, ...), or the division polynomials associated to elliptic curves (elliptic divisibility sequences). In this talk we introduce resultant sequences associated to so-called superelliptic curves and discuss some recent results about them.
   
Friday
 
Serge Fehr
Entropic Quantum Uncertainty Relations
9:00-9:55
We study the intrinsic uncertainty of the measurement outcome when measuring an arbitrary n-qubit quantum state in a basis that is chosen at random from some fixed family of bases. We discuss several canonical cases and obtain (tight) lower bounds on the uncertainty of the measurement outcome, where the uncertainty is measured in terms of the min-entropy. Finally, we briefly point out how these entropic quantum uncertainty relations can be used for proving the security of certain quantum cryptographic schemes.
Cicek Guven Ozcelebi The Collinearity Graph of E7,1 
10:00-10:25
In this talk, we will explain the collinearity graph of the geometry E7,1 in the thin and the thick case. The vertices of this graph has a regular partition. We will look at the distribution diagram of the graph, and knowing the thin case, explain how the parameters of that diagram can be calculated in the thick case by making use of the fact that E7,1 is a parapolar space.
10:30-10:45
coffee
Tobias Müller Line arrangements and geometric representations of graphs
10:50-11:30
I will use some classical results on line arrangements, algebraic geometry and the colin de verdiere number to settle some questions on geometric representations of graphs by Breu&Kirkpatrick, Spinrad, Van Leeuwen & Van Leeuwen and Reiterman et al.
Achill Schürmann
Symmetric polyhedra: from beauty to computational use
11:35-12:30 Polyhedra with symmetries are fascinating objects that occur frequently in mathematics and its applications. They show up in solutions of energy minimization and in symmetric models of optimization problems. In this talk we give a brief survey on existing techniques to exploit symmetries in polyhedral computations and we report on some recent computational successes.
12:30-13:25
lunch
Maxim Hendriks Regular maps and algebraic curves
13:30-13:55
Regular maps are a generalization of the classical regular polyhedra in dimension 2, with the topology of a general closed surface. A remarkable fact is that these surfaces can be made into algebraic curves together with their symmetries. Moreover, relatively nice equations for these `symmetric' curves exist. I will discuss my hunt for such equations belonging to some of these beautiful geometric objects.
Marc Uetz
Graph Theoretic Characterization of Revenue Equivalence
 14:00-14:55 One of the earliest results in the theory of auctions is the famous revenue equivalence theorem. Roughly speaking it states that, under certain assumptions, no matter how an auction is organized, the expected revenue will be the same. There is a long line of papers that derive sufficient conditions under which revenue equivalence holds, not only for auctions, but for the more general concept of mechanisms. We give a surprisingly simple graph theoretic characterization of revenue equivalence for mechanism design, and discuss its usefulness to derive both old and new results.
15:00
tea and aftermath (see also math)


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