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.

November 16th, 2017

Erwin Schrödinger Institute, Boltzmanngasse 9, 1090 Vienna

Preliminary schedule

16:30 Meet&greet (for mathematics&physics) with coffee, tea and sweets

17:00 - 17:10 Opening Remarks

17:10 - 18:30 Panel discussion

18:30 - 19:00 Buffet (wine&beer + sandwiches)

Topic

Relation between the academic world and and its applications, in particular the industry, difference in research/working environment, pressures of publication, difference in research goals, how the collaboration between the two works (both positive and negative aspects), etc.

Speakers

Andrey Krasoovski

http://www.iiasa.ac.at/web/home/research/researchPrograms/EcosystemsServicesandManagement/Krasovskii--Andrey-.en.html

Franz G. Rammerstorfer https://www.ilsb.tuwien.ac.at/~ra/downloads/CV_Rammerstorfer_engl.pdf

Krzysztof Pietrzak https://ist.ac.at/fileadmin/user_upload/pdfs/Faculty_CV_Pubs/Pietrzak_CV.pdf

Moderation

Axel Böhm and Katharina Werbach

Dates:

Monday, October 30th, 13.15 until 16.30, SR2

Wednesday, November 8th, 13.30 until 15.30, SR4

Friday, November 10th, 15.00 until 18.15, SR6

Monday, November 13th, 13.15 until 16.30, SR5

Friday, November 17th, 15.00 until 18.15, SR3

Monday, November 20th, 15.00 until 18.15, SR6

Additional information

Bring a laptop!

Here you can find the slides and the homework, which is divided into different subsections: "required", "recommended" and "optional". You're strongly encouraged to at least look at the problems labeled "required".

Please make sure to have Python 3.6 and Jupyter Notebook installed by the start of the next session (for Windows users it might be easiest to install Anaconda).

Impressions and pictures can be found here https://vd.univie.ac.at/vienna-doctoral-schools/interscience/

For detailed information please visit https://vd.univie.ac.at/vienna-doctoral-schools/interscience/

The School takes place at the Universitätszentrum Obergurgl. Participants are expected to arrive on Saturday, September 2. The programme will start on Sunday, September 3, 9.00 and finish on Thursday, September 7 in the afternoon. Accommodation is in two-bed and three-bed rooms.

Registration: please send an email at your earliest convenience to vds.mathematik@univie.ac.at with information on arrival date and time, departure date and time, and preferred room mates. Deadline for registrations is August 14.

Schedule

Sunday, September 3, 2017

7:30-8:30 Breakfast

8:30-10:00 Henry Cohn *Packing in High Dimensions (I)*

10:00-11:00 Coffee break

11:00-12:30 Josef Teichmann *Affine Processes: Theory, Applications and New Developments (I)*

13:00-15:30 Lunch break

15:30-16:00 Coffee & Cake

16:00-17:00 Henry Cohn *Packing in High Dimensions (II)*

17:30-18:30 Matthias Kreck *A Panorama of Manifolds in Dimensions One to Eight (I)*

19:00 Dinner

20:30 After-Dinner-Talk Josef Teichmann

Monday, September 4, 2017

7:30-8:30 Breakfast

8:30-10:00 Matthias Kreck *A Panorama of Manifolds in Dimensions One to Eight (II)*

10:00-11:00 Coffee break

11:00-12:30 Henry Cohn *Packing in High Dimensions (III)*

13:00-15:30 Lunch break

15:30-16:00 Coffee & Cake

16:00-17:00 Josef Teichmann *Affine Processes: Theory, Applications and New Developments (II)*

17:30-18:30 Henry Cohn *Packing in High Dimensions (IV)*

19:00 Dinner

20:30 After-Dinner-Talk Henry Cohn

Tuesday, September 5, 2017

7:30-8:30 Breakfast

8:30-10:00 Henry Cohn *Packing in High Dimensions (V)*

10:00-11:00 Coffee break

11:00-12:30 Josef Teichmann *Affine Processes: Theory, Applications and New Developments (III)*

13:00 Excursion

19:00 Dinner

20:30 After-Dinner-Talk Matthias Kreck

Wednesday, September 6, 2017

7:30-8:30 Breakfast

8:30-10:00 Josef Teichmann *Affine Processes: Theory, Applications and New Developments (IV)*

10:00-11:00 Coffee break

11:00-12:30 Josef Teichmann *Affine Processes: Theory, Applications and New Developments (V)*

13:00-15:30 Lunch break

15:30-16:00 Coffee & Cake

16:00-17:00 Matthias Kreck *A Panorama of Manifolds in Dimensions One to Eight (III)*

17:30-18:30 Matthias Kreck *A Panorama of Manifolds in Dimensions One to Eight (IV)*

19:00 Dinner

Thursday, September 7, 2017

7:30-8:30 Breakfast

8:30-10:00 Matthias Kreck *A Panorama of Manifolds in Dimensions One to Eight (V)*

10:00-11:00 Coffee break

11:00-12:30 Meeting VDS Students

13:00-15:30 Lunch break

15:30-16:00 Coffee & Cake

16:00-18:00 VDS Discussion

19:00 Social Dinner

Escape Room Game in Vienna

Date: Thursday, June 29^{th}, 2017

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.

Date: Sunday 23rd - Wednesday 26th April 2017

Location: Bundesinstitut für Erwachsenenbildung (bifeb), Strobl, AT

The purpose of this retreat is to bring together the student members of the VDS in a relaxed, friendly atmosphere. The program will consist of a mixture of activities and talks, and all members of the VDS are encouraged to attend and present either some aspect of their research to the other members of the school, or instead something else that is of mathematical interest to them.

The institute is located in beautiful surroundings on the edge of Wolfgangsee, right on the border of Upper Austria and Salzburg:

Talks:

Aigner, Florian: An Interaction of Combinatorics and Statistical Physics: Square Ice, the 6-vertex Model and ASMs

Biberhofer, Sascha: Two Worlds and Inbetween: The Strange Case of Dr. Riemann and Mr. Galois

Chiu, Christopher: The Sounds of the 80s

Cinc, Jernej: Planar Embeddings of Continua

Ender, Christof: Fermat’s Theorem Over Finite Fields

Gilmore, Tomack: The Many Different Faces of a Pile of Cubes

Girsch, Johannes: Combinatorial Nullstellensatz and Applications in Number Theory

Harrach, Christoph: The Erlangen Program

Mejstrik, Thomas: M&M’s Schemes

Saikia, Manjil: Reading Minds and Other Mathematical Stories

Scherl, Daniel: Objects of Catgeories as Complex Numbers (Yes, actually)

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

This event will feature a brief introduction in what this VDS "Mathematics" is going to be, it will feature "general public" lectures by Martin Aigner (FU Berlin) and Karl Sigmund, it will feature posters by the "inaugural" crowd of Ph.D. students in the school (accompanied by coffee and cakes), and, MOST IMPORTANTLY, it will be an OPPORTUNITY for ALL OF US TO COME TOGETHER AND LEARN MORE ABOUT EACH OTHER.