# Events

## VSM Kick-off

### Kick-off Event of the Vienna School of Mathematics

### Wednesday, October 16, 2019 - Grosser Festsaal of the University of Vienna

### Preliminary Schedule:

3.30 – 3.40 pm: Opening address - Univ.-Prof. Dr. Radu Bot (Speaker "Vienna School of Mathematics")

3.40 – 3.50 pm: Opening speech o.Univ.-Prof. Dr. Heinz Engl – Rector of the University of Vienna

3.50 – 4.00 pm: Opening speech o.Univ.-Prof. Dr. Sabine Seidler – Rector of the Vienna University of Technology

4.00 – 4.45 pm: Scientific talk Prof. Dr. Irene Fonseca (Carnegie Mellon University)

4.45 – 5.15 pm: Coffee break

5.15 – 6.00 pm: Scientific talk Prof. Dr. Günter Ziegler (President of FU Berlin)

6.00 pm: Evening reception

# Summer School of the Vienna School of Mathematics, September 22-28, 2019, Weissensee

The School takes place at Hotel Regitnig. Participants are expected to arrive on Sunday, September 22 and to stay until Saturday, September 28. The programme will start on Monday, September 23 in the morning and finish on Friday, September 27 in the afternoon.

To register please fill in the form provided at https://vd.univie.ac.at/vienna-doctoral-schools/mathematics/activities/events/registration-summer-school-2019/ by August 20, 2019.

### Speakers

Alin Bostan, INRIA

Efficient experimental mathematics for combinatorics and number theory

Abstract: Euler, Gauss, Ramanujan, and many other famous mathematicians spent much of their time doing paper-and-pencil computations in order to refine their intuition of the phenomena they studied. George Pólya once wrote that 'Finished mathematics consists of proofs, but mathematics in the making

consists of guesses’. Recent years have seen an explosion of activity in what is now termed "experimental mathematics" or "computer-assisted" mathematics. In its basic form, this activity consists in the use of a computer to look for patterns, to identify particular numbers and sequences, to gather evidence in support of specific mathematical assertions that may themselves arise by computational means. In a more sophisticated form, experimental mathematics is the art of using efficient algorithmic tools for (i) building high-precision approximations of exact mathematical objects, (ii) reconstructing (or, guessing) exact equations from these approximations, (iii) rigorously proving the correctness of the guessed equations. In this series of lectures, I will introduce some experimental mathematics paradigms and show how they can be used to explore and solve a number of beautiful (and sometimes very difficult) questions in enumerative combinatorics and in number theory.

Diogo Gomes, KAUST

An introduction to symbolic mathematics with applications to partial differential equations

Abstract: Often, mathematicians face long and tedious computations. Computer algebra systems routinely simplify complex algebraic equations, compute non-trivial integrals, and solve difficult differential equations. However, these tasks represent only a small fraction of what can be achieved with symbolic mathematics. In this course, I will use the computer algebra system Mathematica to discuss techniques in symbolic programming and their applications. The first part of the course will be a self-contained introduction to Mathematica, with emphasis on functional and rule-based programming. As an application, we will develop a simple partial differential equation solver using the method of characteristics. Then, we examine various applications of quantifier elimination methods - from mathematical olympiad problems to partial differential equations. Finally, we consider problems in partial differential equations and examine how they can be handled by computer algebra. As we will see, multiple non-trivial questions in partial differential equations can be reduced to a mix of linear algebra in the field of rational functions and quantifier elimination. Time permitting, we will discuss the practical implementation, testing and verification techniques, and efficient coding.

Alfio Quarteroni, Politecnico di Milano and Ecole Polytechnique Fédérale de Lausanne (EPFL)

Mathematical and numerical models for multi-physics applications

Abstract: In this series of lectures I will address mathematical models that are suitable for multi-physics applications, where heterogeneous physical processes described by different kind of partial differential equations (PDEs) are coupled. The emphasis will be put on the set up and analysis of numerical strategies that are suitable for the approximation of these problems. Special attention will be devoted to the case of nonconforming approximation, the use of control problems to guarantee the correct coupling of the different PDEs, and the adoption of reduced order models to dominate the computational complexity arising from the presence of multiple sets of parameters (e.g. the model coefficients). Applications will concern fluid dynamics problems, the coupling between surface and subsurface flows, and, more extensively, the simulation of the human cardiovascular system.

## PhD Colloquium

### How does steel deform? An introduction to elastoplastic materials and damage - David Melching

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

For further information please check the following document.

## PhD Colloquium

### An Introduction to Spectral Theory of Laplacians on Graphs - Noema Nicolussi

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

For further information please check the following document.

## PhD Colloquium

### The Importance of Being Totally Disconnected - Giancarlo Castellano

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

For further information please check the following document.

## VDS Mini-course

### Cross-diffusion systems (with Ayman Moussa, Sorbonne Université)

### 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.

## VDS Mini-course

### Evolutionary equations with singular nonlinear terms (with Giulio Schimperna, Università di Pavia)

### 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.

Moreover, I will try to illustrate the theory by applying the results to some specific problems related to physical models from the theory of phase transitions.

## 1st VDS Winter School on Quantum Computation, March 9-15, 2019, Dienten am Hochkönig

The School takes place at Dientnerhof. Participants are expected to arrive on Saturday, March 9. The programme will start on Sunday, March 10 in the morning and finish on Thursday, March 14 in the afternoon.

To register please fill in the form provided at http://vd.univie.ac.at/vienna-doctoral-schools/mathematics/activities/events/registration-winter-school-2019/ by** February 11, 2019**.

Speakers:

Ämin Baumeler (Austrian Academy of Sciences): Introduction to Quantum Computation

Barbara Kraus (Universität Innsbruck): Entanglement Theory

Norbert Schuch (Max Planck Institute of Quantum Optics): Entanglement in Complex Quantum Systems

The schedule can be found here.

## Science Meets: Space

## Science Meets: Space

On 24 January 2019 the third joint VDS Mathematics and Physics "Science meets" event took place in the Schrödinger Lecture Hall at the ESI, Boltzmanngasse 9.

The following speakers were invited for presentation and panel discussion:

- Priv.-Doz. Dr. Friedrich Kupka

Lead Scientist at the Institute of Astrophysics, Faculty of Physics, Georg-August-Universität Göttingen, Germany - Dr. Oliver Jennrich

Fundamental Physics Mission Scientist, and Science Directorate at the European Space Agency (ESA/ESTEC), the Netherlands

Bringing together both mathematical and physics experts resulted in a successful and fruitful exchange.

**Local organizers:**

Yaakov Fein (VDS-P), Dennis Meier (VDS-M), Valeria Milotti (VDS-P), Dang-Khoa Nguyen (VDS-M) and Katharina Werbach (VDS-P).

## PhD Colloquium

### Three-dimensional Motion Reconstruction from Projection Data - Denise Schmutz

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

For further information please check the following document.

## PhD Colloquium

### Geometric Invariants of Surfaces as Natural Objects - Hana Melánová

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

For further information please check the following document.

## PhD Colloquium

### An Introduction to Alternating Sign Matrices (A Combinatorial Story of Missing Bijections) - Florian Aigner

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

For further information please check the following document.

## PhD Colloquium

### Soliton Resolution - When Waves behave like Particles - Mateusz Piorkowski

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

For further information please check the following document.

## VDS Mini-course

### Combinatorics, groups and algebraic varieties (with Fernando Rodriguez Villegas, ICTP (Trieste, Italy)

### 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.

## 3rd VDS Summer School, September 16-22, 2018, Weissensee

The School takes place at Hotel Regitnig. Participants are expected to arrive on Sunday, September 16. The programme will start on Monday, September 17 in the morning and finish on Friday, September 21 in the afternoon.

To register please fill in the form provided at http://vd.univie.ac.at/vienna-doctoral-schools/mathematics/activities/events/registration-summer-school-2018/ by **August 12, 2018**.

The schedule can be found here.

Here you can find the slides of Prof. **László Erdős** as well as problem sheet 1 and problem sheet 2 of **Prof. László Erdős and Dominik Schröder.**

Here you can find the slides of class 1, class 2 and class 3 of Prof. Adolfo Quirós Gracián as well as problem sheet 1 and problem sheet 2 with solutions.

## PhD Colloquium

### What the heck is TQFT? - Daniel Scherl

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

For further information please check the following document.

## Science Meets: Medicine

## Science Meets: Medicine

On 29 May 2018 the second joint VDS Mathematics and Physics "Science meets" event took place in the Schrödinger Lecture Hall at the ESI, Boltzmanngasse 9.

The following speakers were present for the panel discussion:

- DI Manfred Bammer, MAS

Competence Unit Biomedical Systems, Austrian Institute of Technology (AIT) - Marie Doumic, PhD

Wolfgang Pauli Institute, University of Vienna

Inria Paris - Priv.-Doz. Dr. Bianca Gerendas, MSc

Vienna Reading Center, Medical University of Vienna

Christian Doppler Laboratory for Ophthalmic Image Analysis

Bringing together both mathematical and physics experts resulted in a successful and fruitful exchange.

**Local organizers:**

Anna Breger (VDS-M), Yaakov Fein (VDS-P), Manjil Saikia (VDS-M) and Katharina Werbach (VDS-P).

## Transferable Skills Workshop

### Funding Schemes

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

### An introduction for a weak formulation. Why do we look for a weak solution? - Gianluca Favre

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

For further information please check the following document.

## PhD Colloquium

### An Adelic Approach to Number Theory - Paola Lopez

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

For further information please check the following document.

## PhD Colloquium

### Perfect Matchings and Tiling Problems - Manjil Saikia

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

For further information please check the following document.

## VDS Retreat Zwettl

Date: Sunday 4th - Wednesday 7th March, 2018

Location: Hotel Schwarz Alm Zwettl

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 Zwettl in Lower Austria:

## VDS Excursion to Munich, January 24th until January 26th, 2018

WEDNESDAY, JANUARY 24TH:

Departure from Vienna Hauptbahnhof 10.30 am, arrival at Munich Hbf 2.30 pm

Check-in at the hotel

4 pm Guided city tour

6 pm Dinner

Free evening

THURSDAY, JANUARY 25TH:

Morning: Deutsches Museum, guided tour

Lunch at Siemens Munich starting at 12pm

Afternoon (1 until 4pm): guided tour at Siemens

6 pm Dinner

Free evening

FRIDAY, JANUARY 26TH:

10 am Guided tour at BMW Munich (2.5 hours)

Friday afternoon: Departure from Munich Hbf

(c) Picture: Alexander Pichler

## Scientific Python Workshop: Advanced

The workshop focuses on a sound understanding of core libraries, intermediate to advanced language features as well as best practises. The course aims to provide participants with tools and techniques to concisely express their ideas in code and achieve their scientific objectives by means of idiomatic Python.

Instructor: Claus Aichinger, initiator and co-organizer of PyDays Vienna (https://pydays.at/), Austria’s largest Python event.

Dates & Outline:

Monday, January 8th, 15.45 until 18.45, SR6

General Introduction, Technical Setup, NumPy

Friday, January 12th, 15.00 until 18.00, SR3

Pandas, Plotting, Code Style, Patterns and Anti-Patterns

Monday, January 15th, 15.00 until 18.00, SR6

Functions, Classes and OOP, Testing Essentials

Monday, January 22nd, 15.45 until 18.45, SR6

A Data Science / Machine Learning Example

**Prerequisites**

- Bring a laptop!

- What was covered in the introductory course.

- Installed Python 3.6 Anaconda Python distribution (or miniconda)

If you plan to attend, please fill out this form to help fine tune the course content.

## PhD Colloquium

### The d-bar-Neumann problem in several complex variables - Franz Berger

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

For further information please check the following document.

## VDS mini-course

### Spatial Discretizations of Generic Dynamical Systems (with Pierre-Antoine Guihéneuf, IMJ-PRG (Paris 6))

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.

## Science Meets: Applied Academia

## Science Meets: Applied Academia

On 16 November 2017 the first joint VDS mathematics and physics ‘Science’ meets took place in the Schrödinger Lecture Hall at the ESI, Boltzmanngasse 9.

The following speakers were present for the panel discussion:

- Prof. Franz Rammerstorfer

Institute of Lightweight Design and Structural Biomechanics (ILSB), Vienna University of Technology (TU). - Prof. Krzysztof Pietrzak

Institute of Science and Technology (IST) Austria - Dr. Andrey Krasovskii

International Institute for Applied Systems Analysis (IIASA)

Moderated by VDS fellows Axel Böhm and Katharina Werbach, an interesting and interactive discussion about applied science and fundamental research took place. We heard from each of the speakers about their experiences and the advantages and disadvantages of a life dedicated to either one of those sectors. Professor Pietrzak and Dr. Krasovskii, who work on cryptography and mathematical modeling, respectively, shared that they are able to maintain the freedom to set their own scientific goals in their fields of applied research. From Professor Rammerstorfer we learnt more about the Christian Doppler Laboratories and how they bridge the gap between academia and industry.

Bringing together both mathematical and physics experts resulted in a successful and fruitful exchange.

**Local organizers:**

Florian Aigner (VDS-M), Axel Böhm (VDS-M), Yaakov Fein (VDS-P), Daniel Scherl (VDS-M) and Katharina Werbach (VDS-P).

## Python Workshop

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).

## VDS Info Day and PhD Colloquium Tomack Gilmore - Rhombus Tilings and Eletrostatistics

## First Interdisciplinary Symposium of the Vienna Doctoral Schools - September 14-15, 2017

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/

## 2nd VDS Summer School, September 2-8, 2017, Obergurgl

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

## VDS Escape Day

Escape Room Game in Vienna

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

## Transferable Skills Workshop

### Transferable Skills Workshop "How to apply for post-doctoral funding"

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

### Cardinal Invariants of the Continuum and the Structure of the Real Line - Diana Carolina Montoya

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

For further information please check the following document.

## VDS mini-course

### Topological methods in aperiodicity (with James J. Walton)

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.

## VDS mini-course

### An Introduction to Noncommutative Geometry and Quantum Groups (with Réamonn Ó Buachalla)

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

### An Introduction to Symbolic Dynamics - Gabriel Strasser

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

For further information please check the following document.

## VDS mini-course

### A tale of two phenomena: Fixed Point Property and Minimal Dynamical Systems (with Jan P. Boronski)

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.

## VDS mini-course

### Dynamics of the unimodal interval family (with Ana Anusic)

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.

## VDS Retreat Strobl

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

### An Introduction to Multicategories and Higher Categories - Hongyi Chu

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

For further information please check the following document.

## VDS mini-course

### Permutation groups and transformation semi-groups (with Prof. Peter Cameron)

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

### An Introduction to Arithmetic Groups - Sascha Biberhofer

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

For further information please check the following document.

## PhD Colloquium

### Introduction to Optimal Transport - Anastasiia Zalashko

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

For further information please check the following document.

## "Stammtisch"

### Weekly "Stammtisch" for members of the VDS Mathematics

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

## PhD Colloquium

### Introduction to the Nash problem - Christopher Chiu

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

For further information please check the following document.

## PhD Colloquium

### An Introduction to Algebraic Combinatorics - Robin Sulzgruber

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

For further information please check the following document.

## PhD Colloquium

### The singularity theorems of Lorentzian geometry - Melanie Graf

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

For further information please check the following document.

## Summer School

### VDS Summer School, September 18–23, 2016, Obergurgl

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

### Kick-off

#### Kick-off of the Vienna Doctoral School "Mathematics"

### Tuesday, May 17, 2pm, HS14

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.