Events
PhD Colloquium
An introduction to virtual element methods for the Helmholtz problem  Alexander Pichler
PhD Colloquium, June 23rd 2019, 3.00 pm, Sky Lounge, OskarMorgensternPlatz 1.
Please find more information here.
2 pm: VSM Info Day


Kickoff Event of the 

The Vienna School of Mathematics (VSM) is a joint initiative of the doctoral programs in mathematics of the University of Vienna and TU Wien. Its major aim is to promote futureoriented, excellent and autonomous research in the context of doctoral studies. The VSM is targeted at leveraging synergies by generating joint educational structures, creating international visibility, attracting the best doctoral students and integrating them into the local and international research environment.
Speakers
Heinz W. Engl
Sabine Seidler
Irene Fonseca
Günter M. Ziegler
Radu Ioan Boţ
Programme
3.30 pm
The event is open to the public and free of charge.








UNIVERSITÄT WIEN  Universitätsring 1  1010 Wien  T +43142770  www.univie.ac.at 
Summer School of the Vienna School of Mathematics, September 2228, 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/viennadoctoralschools/mathematics/activities/events/registrationsummerschool2019/ by August 27, 2019.
The schedule can be found here.
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 paperandpencil 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 "computerassisted" 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 highprecision 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 nontrivial 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 selfcontained introduction to Mathematica, with emphasis on functional and rulebased 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 nontrivial 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 multiphysics applications
Abstract: In this series of lectures I will address mathematical models that are suitable for multiphysics 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, OskarMorgensternPlatz 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, OskarMorgensternPlatz 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, OskarMorgensternPlatz 1.
For further information please check the following document.
VDS Minicourse
Crossdiffusion systems (with Ayman Moussa, Sorbonne Université)
Timeslots:
Monday, April 1^{st}, 3 pm until 4.30 pm, SR15, 3rd floor, OskarMorgensternPlatz 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:
Crossdiffusion 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 ShigesadaKawasakiTeramoto (SKT, the first instance of crossdiffusion 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 Minicourse
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, OskarMorgensternPlatz 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 nonuniqueness), and longtime 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 915, 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/viennadoctoralschools/mathematics/activities/events/registrationwinterschool2019/ 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, GeorgAugustUniversität 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 (VDSP), Dennis Meier (VDSM), Valeria Milotti (VDSP), DangKhoa Nguyen (VDSM) and Katharina Werbach (VDSP).
PhD Colloquium
Threedimensional Motion Reconstruction from Projection Data  Denise Schmutz
PhD Colloquium, January 16th 2019, 3.00 pm, Sky Lounge, OskarMorgensternPlatz 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, OskarMorgensternPlatz 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, OskarMorgensternPlatz 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, OskarMorgensternPlatz 1.
For further information please check the following document.
VDS Minicourse
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, OskarMorgensternPlatz 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, OskarMorgensternPlatz 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 Lfunctions (particularly those coming from hypergeometric motives), character varieties, combinatorics of quiver representation, etc.
3rd VDS Summer School, September 1622, 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/viennadoctoralschools/mathematics/activities/events/registrationsummerschool2018/ 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, OskarMorgensternPlatz 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 (VDSM), Yaakov Fein (VDSP), Manjil Saikia (VDSM) and Katharina Werbach (VDSP).
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 PostDoctoral 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, OskarMorgensternPlatz 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, OskarMorgensternPlatz 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
Checkin 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 coorganizer 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 AntiPatterns
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 dbarNeumann 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 minicourse
Spatial Discretizations of Generic Dynamical Systems (with PierreAntoine Guihéneuf, IMJPRG (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, OskarMorgensternPlatz 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 (OxtobyUlam) 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, middleterm 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 (VDSM), Axel Böhm (VDSM), Yaakov Fein (VDSP), Daniel Scherl (VDSM) and Katharina Werbach (VDSP).
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 1415, 2017
Impressions and pictures can be found here https://vd.univie.ac.at/viennadoctoralschools/interscience/
For detailed information please visit https://vd.univie.ac.at/viennadoctoralschools/interscience/
2nd VDS Summer School, September 28, 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 twobed and threebed 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
7:308:30 Breakfast
8:3010:00 Henry Cohn Packing in High Dimensions (I)
10:0011:00 Coffee break
11:0012:30 Josef Teichmann Affine Processes: Theory, Applications and New Developments (I)
13:0015:30 Lunch break
15:3016:00 Coffee & Cake
16:0017:00 Henry Cohn Packing in High Dimensions (II)
17:3018:30 Matthias Kreck A Panorama of Manifolds in Dimensions One to Eight (I)
19:00 Dinner
20:30 AfterDinnerTalk Josef Teichmann
Monday, September 4, 2017
7:308:30 Breakfast
8:3010:00 Matthias Kreck A Panorama of Manifolds in Dimensions One to Eight (II)
10:0011:00 Coffee break
11:0012:30 Henry Cohn Packing in High Dimensions (III)
13:0015:30 Lunch break
15:3016:00 Coffee & Cake
16:0017:00 Josef Teichmann Affine Processes: Theory, Applications and New Developments (II)
17:3018:30 Henry Cohn Packing in High Dimensions (IV)
19:00 Dinner
20:30 AfterDinnerTalk Henry Cohn
Tuesday, September 5, 2017
7:308:30 Breakfast
8:3010:00 Henry Cohn Packing in High Dimensions (V)
10:0011:00 Coffee break
11:0012:30 Josef Teichmann Affine Processes: Theory, Applications and New Developments (III)
13:00 Excursion
19:00 Dinner
20:30 AfterDinnerTalk Matthias Kreck
Wednesday, September 6, 2017
7:308:30 Breakfast
8:3010:00 Josef Teichmann Affine Processes: Theory, Applications and New Developments (IV)
10:0011:00 Coffee break
11:0012:30 Josef Teichmann Affine Processes: Theory, Applications and New Developments (V)
13:0015:30 Lunch break
15:3016:00 Coffee & Cake
16:0017:00 Matthias Kreck A Panorama of Manifolds in Dimensions One to Eight (III)
17:3018:30 Matthias Kreck A Panorama of Manifolds in Dimensions One to Eight (IV)
19:00 Dinner
Thursday, September 7, 2017
7:308:30 Breakfast
8:3010:00 Matthias Kreck A Panorama of Manifolds in Dimensions One to Eight (V)
10:0011:00 Coffee break
11:0012:30 Meeting VDS Students
13:0015:30 Lunch break
15:3016:00 Coffee & Cake
16:0018:00 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 postdoctoral funding"
Tuesday, June 20, 2pm, HS7
This workshop is aimed at PhD candidates at the Faculty of Mathematics who will soon be applying for PostDoctoral 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, standalone 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 minicourse
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, OskarMorgensternPlatz 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 minicourse
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), OskarMorgensternPlatz 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 DrinfeldJimbo 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 BorelWeil 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 minicourse
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, OskarMorgensternPlatz 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 minicourse
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, OskarMorgensternPlatz 1
The aim of this mini course is to introduce basic concepts of discrete onedimensional 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
(MilnorThurston kneading theory, full families, formation of periodic orbits and topological entropy)
3. Piecewiselinear model and attractors
(construction of semiconjugacy to tent maps, Markov partitions and substitutions, nonwandering and omegalimit 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 6vertex 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 minicourse
Permutation groups and transformation semigroups (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'NanScott 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 halftime 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 NavierStokes 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 twobed and threebed 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
CoffeeBreak: 10:00
Lunch: 1:00
Coffee & Cake: 3:30
Dinner: 7:00
Monday:
8:30  10:00 Feireisl: The NavierStokes millennium prize problem
11:00  12:30 Landsberg: Uses of geometry in theoretical computer science
4:00  5:00 Cap: Nonholonomic distributions, mechanics, and geometry
5:30  6:30 Schmeiser: Hypocoercivity of the kinetic FokkerPlanck 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 AxGrothendieck Theorem
5:30  6:30 Cap
8:00 AfterDinnerTalk 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 AfterDinnerTalk 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 VDSDiscussion
7:00 Social Dinner
Kickoff
Kickoff 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.