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## Sommersemster 2014

### 05.05.2014 um 16:15 Uhr in 69/E15:

**Martin Gallauer Alves de Souza **(Universität Zürich)

##### Traces in monoidal derivators

I will argue that the additivity of traces should be seen as a principle for which the right context still needs to be found. I will then suggest monoidal triangulated derivators as a candidate for this context. Natural generalizations of the principle

will also be described.

### 06.05.2014 um 16:15 Uhr in 69/125:

#### Dr. Franz Király (University College London)

##### Dual-to-kernel learning with ideals

We propose a theory unifying kernel learning and symbolic algebraic methods. Kernel methods are a very popular class of algorithms employing kernel functions which allow to capture properties of the data in a very efficient way, representing them implicitly in the so-called feature space, the most prominent example being the kernel support vector machine. The main advantage of kernels is also their main downside: since the representation is implicit it has remained an open question what exactly the structures and features are which make the algorithms work.

Symbolic algebraic methods, on the other hand, are by construction structural and deal with the manipulation of explicit equations. So far, their theoretical complexity and intractable computational cost, such as for Gröbner basis computations, has prevented broad application to real-world learning and data analysis.

We show that kernel learning and symbolic algebra are inherently dual to each other, and we use this duality to combine the structure-awareness of algebraic methods with the efficiency and generality of kernels. The main idea lies in relating polynomial rings to feature space, and ideals to manifolds, then exploiting this generative-discriminative duality on kernel matrices. We illustrate this by proposing two algorithms, IPCA and AVICA, for simultaneous manifold and feature learning

### 20.05.2014 um 16:15 Uhr in 69/125:

#### Xuan Thanh Le (Universität Osnabrück)

##### Storage loading problems under uncertainty

The goal of storage loading is to find feasible solutions of stacking uniform items into a storage area such that some stacking constraints are satisfied and some objective functions are optimized. In real-world applications the data of some items are not known exactly, i.e. “under uncertainty”. To guarantee the feasibility of the stacking solutions, we apply the concepts of strict and adjustable robustness. In this talk, complexity results and solution methods for solving strictly and adjustable robust counterparts of some storage loading problems under uncertainty are presented.

### 03.06.2014 um 16:15 Uhr in 69/125:

#### Prof. Dr. Serkan Hosten (San Francisco)

##### The degree of the central curve in quadratic programming

For convex optimization problems, such as linear, quadratic, or semidefinite programming, a class of interior point algorithms track the so-called central path to an optimal solution. The central curve, the Zariski closure of the central path, is an algebraic curve and it has been recently studied by De Loera, Sturmfels, and Vinzant in the linear case. In particular, the degree of the central curve for linear programming has been computed, and this has implications for the complexity of the interior point algorithms. We tackle the next case, the degree of the central curve for quadratic programming. After a reduction to the "diagonal" case, we conjecture a formula and present a strong case for the conjecture. Also, in the diagonal case, we construct a Groebner basis for the ideal defining the central curve.

### 17.06.2014 um 16:15 Uhr in 69/125:

#### Prof. Dr. H. Michael Möller (Universität Dortmund)

##### Stetter's eigenvector method

Using companion matrices one can transform the problem of computing thezeros of a univariate polynomial into an eigenproblem. Using the multivariate generalization of companion matrices, Stetter transformed the problem of solving systems of polynomial equations into the problem ofcomputing eigenspaces. In this talk, we present his method and show modifications of his algorithm.

### 01.07.2014 um 16:15 Uhr in 69/125:

#### Prof. Dr. Zbigniew Fiedorowicz (Ohio State University)

##### Realizing Iterated Loop Spaces as Categories

Realizing Iterated Loop Spaces as CategoriesSince the work of Quillen on algebraic K-theory in the 1970's, there has been a fruitful interaction betweenalgebraic structures on categories and algebraic K-theory and algebraic structures in homotopy theory. Typically one starts with such a structured category and converts it into a space or spectrum which onethen analyzes with the tools of homotopy theory. We have been interested in the inverse problem: given a space with such a structure, can we associate to it a category with an appropriate algebraic structure?One of my long term projects with my coworkers in this Fachbereich has been to realize this program for iterated loop spaces. The categorical analog of this structure is the notion of iterated monoidal category.We have recently succeeded in carrying out the last step of this program, and in this talk I will describe some of the ideas we used to achieve this.

### 15.07.2014 um 16:15 Uhr in 69/125:

#### Gilles Bonnet (Universität Osnabrück)

##### Small cells in a random hyperplane mosaics

We will explain what is the typical cell of a random stationary hyperplane mosaic in [image: \mathbb{R}^d] and investigate its distribution. We will see how are related the distributions of the number of facets, the size and the shape of the typical cell. Finally we give some asymptotic results for the distribution of small cells.

### 02.09.2014 um 16:15 Uhr in 69/125:

#### Prof. Dr. H. Michael Möller (Universität Dortmund)

##### Multivariate polynomial interpolation with disturbed points

Given a finite set *X* of real n-tuples (points), one may ask for polynomials *p* which belong to a subspace V and which attain given values at the points of *X*. We focus on subspaces *V* generated by low degree monomials. Using QR decmpositions we present an algorithm which is more stable than the original Buchberger-Moeller algorithm (1982). If *X* contains only disturbed points, the homogeneous interpolation problem is replaced by the problem of finding (normalized) polynomials minimizing the ∑_{uЄX} p(u)^{2}. Such polynomials can be found as byproduct in the QR decompositions of the new algorithm.

### 16.09.2014 um 10:00 Uhr in 69/125:

#### Utsav Choudhury (Universität Osnabrück)

##### An isomorphism of motivic Galois group

The conjectural category of mixed motives is supposed to satisfy several conditions. One of the condition is that it should be a representation category of a Group scheme, the so called motivic Galois group. Just as the original Grothendieck-Galois correspondence is useful in that it translates questions of finite separable field extensions into questions of profinite groups and their representations, so does the Tannakian formalism for motives translate geometric questions of algebraic varieties into questions of motivic Galois group and its representations.

This picture is still purely conjectural. However, there are candidates for motivic Galois groups. In this talk I will describe how to compare two such candidates (motivic Galois group constructed by M.Nori and motivic Galois group constructed by J. Ayoub).

### 24.09.2014 um 16:00 Uhr in 69/125:

**Prof. Dr. Ngô Việt Trung** (Institute of Mathematics, Hanoi)

##### Associated primes of powers of edge ideals

We present a complete combinatorial classification of the associated primes of every fixed power of the edge ideal of a graph.

This will be done by using matching theory. It turns out that these associated primes are characterized by certain kind of subgraphs