PhD Colloquium, June 23rd 2019, 3.00 pm, Sky Lounge, Oskar-Morgenstern-Platz 1.

Please find more information here.

2 pm: VSM Info Day

PhD Colloquium, June 19th 2019, 2.00 pm, Sky Lounge, Oskar-Morgenstern-Platz 1.

For further information please check the following document.

PhD Colloquium, May 22nd 2019, 3.00 pm, Sky Lounge, Oskar-Morgenstern-Platz 1.

For further information please check the following document.

PhD Colloquium, April 10th 2019, 3.00 pm, Sky Lounge, Oskar-Morgenstern-Platz 1.

For further information please check the following document.

Timeslots:

Monday, April 1^st, 3 pm until 4.30 pm, SR15, 3rd floor, Oskar-Morgenstern-Platz 1
Tuesday, April 2nd, 10.30 am until 12.00 pm, SR11, 2nd floor, OMP1
Wednesday, April 3rd, 10.30 am until 12.00 pm, SR5, 1st floor, OMP1
Thursday, April 4th, 10.30 am until 12.00 pm, SR5, 1st floor, OMP1
Friday, April 5^th, 9 am until 10.30 am, SR14, 2nd floor, OMP1

Abstract:

Cross-diffusion systems where introduced 40 years ago as a tool of modeling in the context of population dynamics. At the mathematical level, these systems happen to be surprisingly hard to study ; global (weak) solutions for the most simple of those were (only) built in 2006 even though they have been studied since the eighties.

We will start this lecture with a short introduction to present the model of Shigesada-Kawasaki-Teramoto (SKT, the first instance of cross-diffusion in the literature) and present (without proof) the existing results and the open questions related to it. Then, in the first part of the lecture, we will focus on the Kolmogorov equation, studying existence and uniqueness with the help of the duality lemma. In the second part of the lecture we will establish a global existence result for SKT systems, using a generalization of the entropy introduced by Chen and Jüngel in 2006, the duality lemma and a specific approximation procedure.

The lecture notes can be found here.

Timeslots:

Monday, March 25^th, 3 pm until 4.30 pm, SR16, 3rd floor, Oskar-Morgenstern-Platz 1
Tuesday, March 26^th, 1.15 pm until 2.45 pm, SR13, 2nd floor, OMP1
Wednesday, March 27^th, 1.15 pm until 2.45 pm, SR13, 2nd floor, OMP1
Thursday, March 28^th, 1.15 pm until 2.45 pm, SR15, 3rd floor, OMP1

Abstract:

After recalling a number of basic notions from convex analysis (maximal monotone operators, subdifferentials), I will focus on some mathematical aspects of evolutionary partial differential equations characterized by the presence of singular (i.e., very fastly growing) terms. I will discuss existence of solutions, regularity properties, uniqueness (or non-uniqueness), and long-time behavior.

PhD Colloquium, January 16th 2019, 3.00 pm, Sky Lounge, Oskar-Morgenstern-Platz 1.

For further information please check the following document.

PhD Colloquium, December 5th 2018, 3.00 pm, Sky Lounge, Oskar-Morgenstern-Platz 1.

For further information please check the following document.

PhD Colloquium, November 14th 2018, 3.00 pm, Sky Lounge, Oskar-Morgenstern-Platz 1.

For further information please check the following document.

PhD Colloquium, October 31st 2018, 3.00 pm, Sky Lounge, Oskar-Morgenstern-Platz 1.

For further information please check the following document.

Timeslots:

Monday, November 5th, 9.30 am until 11.00 am, SR16, 3rd floor, Oskar-Morgenstern-Platz 1
Wednesday, November 7th, 9.30 am until 11.00 am, SR15, 3rd floor, OMP1
Thursday, November 8th, 9.30 am until 11.00 am, SR15, 3rd floor, OMP1
Monday, November 12th, 9.30 am until 11.00 am, SR15, 3rd floor, OMP1
Wednesday, November 14th, 9.30 am until 11.00 am, SR16, 3rd floor, Oskar-Morgenstern-Platz 1

Abstract:

In this course we will discuss how techniques from enumerative combinatorics and the representation theory of finite groups can be used to study the geometry of certain algebraic varieties. Examples will include some character varieties as well as some related quiver varieties. We will introduce all the basic theory needed from scratch.

Speaker:

Professor Fernando Rodriguez Villegas is a Senior Research Scientist at the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, Italy.  His research interests lies in number theory, in the study of L-functions (particularly those coming from hypergeometric motives), character varieties, combinatorics of quiver representation, etc.

PhD Colloquium, June 6th 2018, 1.45 pm, HS 10, Oskar-Morgenstern-Platz 1.

For further information please check the following document.

Thursday, May 17, 2018, 3pm, HS11 (OMP1)

Barbara Leitner (Forschungsservice und Nachwuchsförderung) and Harald Schwab (projektSERVICE Mathematik)

This workshop is aimed at PhD candidates at the Faculty of Mathematics who will soon be applying for Post-Doctoral funding. It is an informative workshop on international and national funding opportunities
with a particular focus on the FWF Schrödinger Scholarship.

PhD Colloquium, May 16th 2018, 1.45 pm, HS 10, Oskar-Morgenstern-Platz 1.

For further information please check the following document.

PhD Colloquium, April 18th 2018, 1.30 pm, HS 16, Oskar-Morgenstern-Platz 1.

For further information please check the following document.

PhD Colloquium, March 21^st 2018, 3.00 pm, Sky Lounge

For further information please check the following document.

PhD Colloquium, November 15^th 2017, 3:00 pm, SR13

For further information please check the following document.

Date: Monday, November 20th, 10.00 until 11.30

Tuesday, November 21st, 15.00 until 16.30

Wednesday, November 22nd, 15.00 until 16.30

Thursday, November 23rd, 15.00 until 16.30

Friday, November 24th, 15.00 until 16.30

Location: Monday until Wednesday SR 13, Thursday SR 16, Friday SR 10, Oskar-Morgenstern-Platz 1

Abstract

How is it possible to read dynamical properties of a system on numerical simulations? The computer working with finite numerical precision, it replaces the dynamics f by a spatial discretization f_N (where stands for the numerical accuracy, e.g. the number of binary digits). We will be interested in the dynamical behaviour of the finite maps f_N for a generic system f and N going to infinity (mainly among sets of homeomorphisms or C^{^1}-diffeomorphisms). These lectures will be enlightened by numerical simulations, and will also be the occasion to understand some tools of generic dynamics.

Schedule

Day 1: Presentation of the problem. Ergodic behaviour of generic homeomorphisms.
Day 2: Generic conservative homeomorphisms: periodic approximation, applications to genericity results (Oxtoby-Ulam) and discretizations. Application to numerical computation of rotation sets.
Day 3: Discretizations of linear maps: quasicrystals, Minkowski theorem and application to numerical image rotation problem.
Day 4: Generic C^{^1}-diffeomorphisms: local/global formula, physical measures via some tools of C^{^1} perturbations.
Day 5: Lanford and Hilbert's sixth problem, middle-term behaviour of discretizations.

Tuesday, June 20, 2pm, HS7

This workshop is aimed at PhD candidates at the Faculty of Mathematics who will soon be applying for Post-Doctoral funding. It is an informative workshop on international and national funding opportunities
with a particular focus on the relevant funding schemes from the Austrian Science Fund (FWF) e.g. Erwin Schrödinger outgoing fellowship, Hertha Firnberg, stand-alone projects etc. and the Individual Fellowships scheme within the European Union’s Marie Skłodowska Curie Actions (MSCA programme).

PhD Colloquium, June 7^th 2017, 3:15pm, HS05

For further information please check the following document.

Date: Wednesday, June 7th, 11.30 until 13.30

Thursday, June 8th, 11.30 until 12.30

Friday, June 9th, 11.30 until 13.30

Location: Wednesday and Thursday SR 4, Friday SR 3, Oskar-Morgenstern-Platz 1

Schedule

7th June 11.30 until 13.30 (2 hours): Aperiodic order

The idea of aperiodic order, introduced through examples and applications. The two main approaches to constructing aperiodic patterns: substitution and the cut and project method. Interactions of aperiodic order and number theory through the cut and project method, and selected review of some more general directions in the field of aperiodic order.

8th June 11.30 until 12.30 (1 hour): Pattern spaces

How one associates to a pattern a moduli space of associated patterns: the translational hull of an FLC pattern. Basic topological and dynamical properties of the translational hull. Presentations as inverse limits of approximants.

9th June 11.30 until 13.30 (2 hours): Pattern cohomology

Elementary introduction to cellular cohomology and Cech cohomology. Example computations of Cech cohomology groups of some pattern spaces, along with discussion of more general approaches. Visualising pattern cohomology through pattern equivariance. Applications of pattern cohomology and discussion on future directions and open problems.

Here are the notes.

Date: Monday, May 29 until Friday, June 2, 11.00 until 12.30

Location: Meeting Room 2nd floor (BZ02), Oskar-Morgenstern-Platz 1

Abstract: We begin this series of lectures with an introduction to the general theory of Hopf algebras, their relationship to classical algebraic groups, and the definition of Drinfeld-Jimbo quantised enveloping algebras. The notion of a quantum homogeneous space is then introduced and the classical equivalence between equivariant vector bundles and representations of the isotropy subgroup is shown to carry over to the noncommutative setting. This brings us naturally to the notions of covariant differential calculi, noncommutative complex structures, and noncommutative K\"ahler structures. Throughout, the Podle\'s sphere, or the quantum projective line, is used as a motivating example. Moreover, the natural $q$-deformed Dirac operator associated to the Podle\'s sphere is used to introduce the theory of spectral triples and the $C^*$-algebraic approach to noncommutative geometry. We finish by looking at the Borel--Weil theorem for the Podle\'s sphere and give a brief introduction to the theory of noncommutative projective algebraic geometry.

PhD Colloquium, May 17^th 2017, 3:15pm, HS05

For further information please check the following document.

Date: Tuesday, May 16th until Friday, May 19th

Time: 10:00 - 11:00

Location: Tuesday, Wednesday and Friday SR 6, Thursday HS 7, Oskar-Morgenstern-Platz 1

Schedule

Tue May 16 (10.00 - 11.00 a.m.):
A. Introduction to minimal systems and minimal spaces: minimal Cantor systems, irrational circle rotations, minimal sets.
B. Minimality vs. local versions of Banach Fixed Point Theorem.

Wed May 17 (10.00 - 11.00 a.m.):
A. Minimality in Cartesian products.

Thu May 18 (10.00 - 11.00 a.m.):
A. Introduction to Fixed Point Theory.
B. Fixed Point Theorems for Planar Homeomorphisms Part 1.

Fri May 19 (10.00 - 11.00 a.m.):
A. Fixed Point Theorems for Planar Homeomorphisms Part 2 and beyond.

More detailed information can be found here.

The notes can be found here.

Date: Wednesday 3rd - Friday 5th May, 2017

Time: 15:00 - 17:00

Location: Wednesday SR15, Thursday and Friday SR13, Oskar-Morgenstern-Platz 1

The aim of this mini course is to introduce basic concepts of discrete one-dimensional dynamical systems through the unimodal family of interval maps. We primarily focus on topological, symbolic and combinatorial aspects of the theory.

1. Bifurcation diagram of the logistic family, Feigenbaum universality and chaos
(asymptotic behavior of orbits of logistic maps, hyperbolicity and bifurcations, renormalization, Feigenbaum constants and chaos)

2. Symbolic dynamics and kneading theory for unimodal maps
(Milnor-Thurston kneading theory, full families, formation of periodic orbits and topological entropy)

3. Piecewise-linear model and attractors
(construction of semi-conjugacy to tent maps, Markov partitions and substitutions, nonwandering and omega-limit sets, attractors of unimodal maps)

Ana Anusic, Faculty of Electrical Engineering and Computing, University of Zagreb.

The notes can be found here.

PhD Colloquium, April 5^th 2017, 3pm, Sky Lounge

For further information please check the following document.

Date: Monday 20th - Friday 24th March 2017

Time: 10:00 - 12:00

Location: BZ03

The course will be in five short sections:
  --  Introduction to semigroups (basic concepts of semigroup theory, examples
      of semigroups, analogues of Cayley's theorem)
  --  Permutation groups: Orbits and transitivity, blocks and primitivity,
      O'Nan-Scott theorem and applications of CFSG, groups and graphs
  --  Synchronization and graph endomorphisms: the \v{C}ern\'y conjecture,
      connection with graph endomorphisms, examples, open problems
  --  Regularity and idempotent generation: connection with partition
      transversals, applications of CFSG, the road closure problem
  --  Chains of subsemigroups: results for symmetric group and symmetric
      inverse semigroup, partial results for the full transformation monoid

Here is some information about Professor Cameron taken from his wikipedia page:

Peter Jephson Cameron (born 23 January 1947) is an Australian mathematician who works in group theory, combinatorics, coding theory, and model theory. He is currently half-time Professor of Mathematics at the University of St Andrews, and Emeritus Professor at Queen Mary University of London. Cameron received a B.Sc. from the University of Queensland and a D.Phil. in 1971 from University of Oxford, with Peter M. Neumann as his supervisor.[3] Subsequently he was a Junior Research Fellow and later a Tutorial Fellow at Merton College, Oxford, and also lecturer at Bedford College, London. He was awarded the London Mathematical Society's Whitehead Prize in 1979 and is joint winner of the 2003 Euler Medal. Cameron specialises in algebra and combinatorics; he has written books about combinatorics, algebra, permutation groups, and logic, and has produced over 250 academic papers.[4] He posed the Cameron–Erdős conjecture with Paul Erdős.

Here are the notes.

PhD Colloquium, March 15^th 2017, 3pm, Sky Lounge

For further information please check the following document.

PhD Colloquium, January 18^th 2017, 3pm, Sky Lounge

For further information please check the following document.

Taking place every Thursday at 7 pm at Lichtenthaler Bräu (Liechtensteinstrasse 108), unless otherwise specified.

PhD Colloquium, December 14^th 2016, 3pm, Seminar room 3

For further information please check the following document.

PhD Colloquium, November 23^rd 2016, 3pm, Sky Lounge

For further information please check the following document.

PhD Colloquium, October 19^th 2016, 3pm, Sky Lounge

For further information please check the following document.

This School will feature the following two courses:

Eduard Feireisl (Charles University Prague): The Navier-Stokes millennium prize problem

Joseph M. Landsberghttp://www.math.tamu.edu/~jml/ (Texas A&M University, College Station): Uses of geometry in theoretical computer science

The programme will be complemented by short lectures by the organisers.

The School takes place at the Universitätszentrum Obergurgl. Participants are expected to arrive on Sunday, September 18. The programme will start on Monday, September 19, 9.00 and finish on Friday, September 23 in the afternoon. Accommodation is in two-bed and three-bed rooms. The cost for board and lodging is €89,50 per day.

Organisers: Radu Ioan Boţ, Andreas Čap, Herwig Hauser, Josef Hofbauer, Christian Krattenthaler, Christian Schmeiser, Joachim Schwermer

Registration: please send an email at your earliest convenience to bettina.hiebl@univie.ac.at with information on arrival date and time, departure date and time, and preferred room mates. Deadline for registrations is August 15.

Program VDS Summer School, Obergurgl September 19 - 23, 2016 

Arrival, afternoon Sunday September 18

Buses from Oetztal Bahnhof to Obergurgl depart at 3:10, 3:45, 4:48, 6:18, 7:35 pm, travel time 90 min.

Breakfast:           7:30 - 8:30

Coffee-Break:    10:00

Lunch:                 1:00

Coffee & Cake:  3:30

Dinner:                7:00

Monday:

8:30 - 10:00     Feireisl: The Navier-Stokes millennium prize problem

11:00 - 12:30   Landsberg: Uses of geometry in theoretical computer science

4:00 - 5:00       Cap: Non-holonomic distributions, mechanics, and geometry

5:30 - 6:30       Schmeiser: Hypocoercivity of the kinetic Fokker-Planck equation

Tuesday:

8:30 - 10:00     Feireisl

11:00 - 12:30   Landsberg

4:00 - 5:00       Hauser: The Jacobian conjecture about polynomial automorphisms and the Ax-Grothendieck Theorem

5:30 - 6:30       Cap

8:00                  After-Dinner-Talk Feireisl (optional)

Wednesday:

8:30 - 10:00     Feireisl

11:00 - 12:30   Landsberg

4:00 - 5:00       Feireisl

5:30 - 6:30       Hauser 

8:00                  After-Dinner-Talk Landsberg (optional)

Thursday:

8:30 - 10:00     Feireisl

11:00 - 12:30   Landsberg

1:00 - 6:00       Excursion

Friday:

9:00 - 10:00     Schmeiser

11:00 - 12:30   Landsberg

4:00 - 6:00       VDS-Discussion

7:00                  Social Dinner

Tuesday, May 17, 2pm, HS14