Fachgebiet Algorithmische AlgebraKolloquium (Oberseminar)

# Kolloquium

In unserem Kolloquium algorithmische Mathematik und Komplexitätstheorie tragen Mitarbeiter und Gäste über aktuelle Themen ihrer Forschung vor.

Das Oberseminar findet donnerstags von 14:15 bis etwa 15:45 Uhr im Raum MA 316 statt.

# Terminplan

Geplante Vorträge
Vortragender
Titel
Datum
Zeit
Prof. Dr. Peter Bürgisser
Condition of intersecting a projective variety with a varying linear subspace

This talk will be informal. People attending this talk are required to have some basic knowledge about condition in numerical analysis.
22.10.15
14:15
Jesko Hüttenhain
Orbit Closures of homogeneous Forms
05.11.15
14:15
Maurice Rojas (Texas A&M)
On a Real Analogue of Smale's 17th Problem
26.11.15
14:15
Dr. Pierre Lairez
TBA
03.12.15
14:15
Jerzy Weyman
On the minimal free resolutions of the ideal generated by $k\times k$ subpermanents of an $n\times n$ matrix.
21.01.16
14:15
Josué Tonelli Cueto
Gurvits' algorithm and its application to non-commutative RIT: An overview of a result of Garg, Gurvits, Oliveira and Wigderson
04.02.16
14:15
Jesko Hüttenhain
Polynomial degree bounds for matrix semi-invariants
11.02.16
14:15

# Abstracts

Hier finden Sie die Zusammenfassungen der geplanten Vorträge.

## On a Real Analogue of Smale's 17th Problem

Donnerstag, 26. November 2015

Speaker: J. Maurice Rojas

The recent solution to Smale's 17th Problem tells us that, under a particular model of randomness, one can find an approximate complex root, to an $n$ by $n$ system of polynomials of degree d, on average, in time polynomial in $(n+d)^{\min \{d,n\} }$. However, much less is known about the average-case complexity of finding approximate real roots. And before looking for approximate real roots, one should first determine whether there are even any real roots.

To address the latter question, we give results on $A$-discriminants indicating the possibility of counting real roots in time polynomial in $\log d$, on average, when $n$, and the number of monomial terms, are fixed.

## Orbit Closures of homogeneous Forms

Speaker: Jesko Hüttenhain

The general linear group $\operatorname{GL}_n$ acts by precomposition on the space of homogeneous forms $\mathbb C[x_1,\ldots,x_n]_d$ of degree $d$. We consider the orbit of a form $P$ - under mild conditions, this orhbit and its Zariski closure differ by a divisor $D$. We present methods to find components of this divisor and some ideas on how to bound the number of components from above. In some very special cases, this can be used to completely describe the components of $D$.

## On the minimal free resolutions of the ideal generated by $k\times k$ subpermanents of an $n\times n$ matrix.

Speaker: Jerzy Weyman

I will review the results of my joint paper with Efremenko. Landsberg and Schenck (ArXiv:1504.0517) on the polynomial relations between $k\times k$ subpermanents of an $n\times n$ matrix. I will try to give the background and the feeling for the algebraic techniques we used.