Sunrise over Lake Konstanz (by Philipp di Dio, 9th of November 2023, 7:02)

MoPAT-24 – Moments and Polynomials: Applications and Theory

11th to 14th of March 2024, Konstanz

Sunrise over Lake Konstanz (by Philipp di Dio, 14th of August 2023, 6:32)

MoPAT-24 – Moments and Polynomials: Applications and Theory

The interplay and connection between the theory of moments and polynomials was always strong, almost inseparable, and probably no theory would be able to evolve without the other.

In this conference we want to bring both aspects together again by looking at past, present, and hopefully future developments. The topics shall not only cover the classical theory of moments and polynomials, but also look into matrix moments and polynomials as well as applications.

Organized by Philipp di Dio and Tobias Sutter.


About the Organizers

Philipp J. di Dio (Main Organizer)

Philipp di Dio is a 5 Year Research Fellow (research group leader) at the Zukunftskolleg (Institute for Advanced Studies) with his own group since 2022. He studied chemistry and mathematics at the second oldest German university, the University of Leipzig founded 1409. After his bachelor in chemistry and his diploma in mathematics he did his PhD under supervision of Konrad Schmüdgen on the moment problem as a member of the Max Planck Institute for Mathematics in the Science in Leipzig with a PhD-scholar ship. He did a PostDoc at the TU Berlin under supervision of Mario Kummer and at the LAAS-CNRS in Toulouse under supervision of e.g. Jean-Bernard Lasserre. With his DFG grant he joined in 2022 the University of Konstanz and the Zukunftskolleg where he works on the interplay between moments, polynomials, and partial differential equations.

Tobias Sutter (Co-Organizer)

Tobias Sutter is tenure-track-professor for Computer Science with focus on Machine Learning at the University of Konstanz since 2021. Since 2022 he is a member of the Centre for Human | Data | Society. He received his bachelor’s degree in 2007 on a thesis of Mechanical Engineering at the ETH Zürich (Switzerland), followed by the master’s degree in 2012. In 2017 he earned a PhD in Electrical Engineering (thesis: Convex programming in optimal control and information theory). After postdoctoral research positions at EPF Lausanne and ETH Zürich he is now Fellow of the Institute for Advanced Study at the University of Konstanz. He is Group leader at the Cluster of Excellence: Centre for the Advanced Study of Collective Behaviour and Program Committee of the Annual Learning for Dynamics & Control Conference (L4DC). His research is focused on Machine Learning, Stochastic Optimization and Control and Information Theory.

Island of Mainau (by Philipp di Dio, 19th of November 2023)

Invited Speaker

Hamza Fawzi (University of Cambridge)

Jean-Bernard Lasserre (LAAS-CNRS Toulouse)

Monique Laurent (CWI Amsterdam and Tilburg University)

Tim Netzer (University of Innsbruck)

Konrad Schmüdgen (University of Leipzig)

Markus Schweighofer (University of Konstanz)

Jan Stochel (Jagiellonian University, Krakow)


List of Participants

Baldi, Lorenzo (Max Planck Institute for Mathematics in the Sciences, Leipzig)
Blomenhofer, Alexander Taveira (CWI Amsterdam)
Brüser, Clemens (TU Dresden)
Brosch, Daniel (University of Klagenfurt)
Cimpric, Jaka (University of Ljubljana)
di Dio, Philipp (University of Konstanz)
Eggen, Carl (University of Konstanz)
El Azhar, Hamza (Chouaib Doukkali University, Morocco)
van der Eyden, Mirte (University of Innbruck)
Fawzi, Hamza (University of Cambridge)
Garloff, Jürgen (University of Konstanz and HTWK Konstanz)
Grunwald, Rüdiger (University of Konstanz)
Gutschlag, Theodor (University of Konstanz)
Hess, Sarah-Tanja (University of Konstanz)
Jablonski, Zenon (Jagiellonian University, Krakow)
Kaiser, Marcel (University of Konstanz)
Klingler, Andreas (University of Innsbruck)
Kovalyov, Ivan (University of Osnabrück)
Kozhasov, Khazhgali (Université Côte d’Azur, Nice)
Krapp, Lothar Sebastian (University of Konstanz)
Langer, Lars-Luca (University of Konstanz)
Lasserre, Jean-Bernard (LAAS-CNRS Toulouse)
Laurent, Monique (CWI Amsterdam and Tilburg University)
Metzlaff, Tobias (University of Kaiserslautern-Landau)
Michalek, Mateusz (University of Konstanz)
Miller, Jared (ETH Zurich)
Netzer, Tim (University of Innsbruck)
Pietrzycki, Pawel (Jagiellonian University, Krakow)
Ríos-Zertuche, Rodolfo (UiT The Arctic University of Norway, Tromsø)
Salac, Radek (University of Konstanz)
Sawall, David (University of Konstanz)
Schick, Moritz (University of Konstanz)
Schmüdgen, Konrad (University of Leipzig)
Schötz, Matthias (Polish Academy of Sciences)
Schweighofer, Markus (University of Konstanz)
Slot, Lucas (ETH Zurich)
Stochel, Jan (Jagiellonian University, Krakow)
Sun, Shengding (University of Cambridge)
Sutter, Tobias (University of Konstanz)
Vargas, Luis Felipe (IDSIA Lugano)
Zalar, Aljaz (University of Ljubljana)

If you don't find your name on the list, please let us know.

Talks & Abstracts

You find here as PDF the list of participants and talks with abstracts. "jww" = "joint work with"

1. Baldi, Lorenzo (jww Greg Blekherman and Rainer Sinn)
Carathéodory numbers and flat extension for measures supported on genus one curves

2. Blomenhofer, Alexander Taveira (jww Alex Casarotti)
Nondefectivity of invariant secant varieties

3. Brüser, Clemens (jww Mario Kummer)
Quadratic Determinantal Representations of Positive Polynomials

4. Brosch, Daniel
Combinatoric derivations in extremal graph theory and Sidorenko's conjecture

5. Eggen, Carl (jww Oliver Stein and Stefan Volkwein)
Granularity for mixed-integer polynomial optimization problems

6. van der Eyden, Mirte
Beyond free spectrahedra

7. El Azhar, Hamza
On the square root problem

8. Fawzi, Hamza
TBA

9. Jablonski, Zenon (jww Piotr Budzynski, Il Bong Jung and Jan Stochel)
Subnormality via moments

10. Klingler, Andreas (jww Tim Netzer)
A homotopy method for convex optimization

11. Kovalyov, Ivan
A truncated indefinite Stieltjes moment problem

12. Kozhasov, Khazhgali (jww Greg Blekherman, Pablo Parrilo, Bruce Reznick and Isabelle Shankar)
When are odd powers of non-negative forms SOS?

13. Krapp, Lothar Sebastian (jww Merlin Carl)
Schanuel's Conjecture, Roots of Exponential Polynomials and Peano Arithmetic

14. Lasserre, Jean-Bernard
The Christoffel function: New applications, connections and extensions

15. Laurent, Monique
Sums of Squares of Polynomials for Matrix Copositivity and Stable Sets in Graphs

16. Metzlaff, Tobias (jww Evelyne Hubert, Philippe Moustrou, and Cordian Riener)
Chebyshev Moments

17. Michalek, Mateusz
Enumerative geometry meets statistics and optimization

18. Miller, Jared (jww Chiara Meroni, Matteo Tacchi, and Mauricio Velasco)
Maximizing Slice-Volumes of Semialgebraic Sets using Sum-of-Squares Programming

19. Netzer, Tim (jww Maximilian Illmer and Andreas Thom)
Zeros of Polynomial Equations in Matrices, Quaternions and Beyond

20. Pietrzycki, Pawel (jww Jan Stochel)
Operator moments and Arveson's hyperrigidity

21. Ríos-Zertuche, Rodolfo (jww Didier Henrion, Milan Korda, and Martin Kruzík)
Relaxation gaps for SDP-based algorithms for PDEs and optimal control

22. Sawall, David (jww Mario Kummer)
Amalgamation of real zero polynomials with two common variables

23. Schick, Moritz
Quantitative relation of the cones of sums of squares and sums of nonnegative circuit polynomials

24. Schmüdgen, Konrad
The matricial truncated moment problem

25. Schötz, Matthias (jww Philipp Schmitt)
Real Nullstellensatz for 2-step nilpotent Lie algebras

26. Schweighofer, Markus (jww Luis Vargas)
Pure states for polynomial nonnegativity certificates in the presence of zeros

27. Slot, Lucas (jww Jean-Bernard Lasserre)
Rational Christoffel functions for measures with conditional independence

28. Stochel, Jan
Moment problem for discrete measures via idempotents

29. Sun, Shengding (jww Greg Blekherman, Mario Kummer, Raman Sanyal and Kevin Shu)
Generalizing determinantal inequalities using linear prinicipal minor (lpm) polynomials

30. Vargas, Luis Filipe
Complexity Results About the Exactness of Sum-of-Squares Approximations for Polynomial Optimization

31. Zalar, Aljaz (jww Igor Klep and Tea Strekelj)
A gap between positive even quartics and sums of squares ones

If you don't find your talk/abstract here and/or the PDF, please let us know.

Program

Your find the program, talks, and abstracts also here as PDF.

Monday, March 11th 2024
Room K503

10.00 - 10.20 Arrival
10.25 - 10.30 Philipp di Dio and Tobias Sutter
Greetings and Opening
10.35 - 11.20 Konrad Schmüdgen
The matricial truncated moment problem
11.25 - 11.55 Pawel Pietrzycki
Operator moments and Arveson's hyperrigidity

12.00 - 13.30 Lunch and Coffee

13.30 - 14.15 Monique Laurent
Sums of Squares of Polynomials for Matrix Copositivity and Stable Sets in Graphs
14.20 - 15.05 Markus Schweighofer
Pure states for polynomial nonnegativity certificates in the presence of zeros
15.10 - 15.30 Coffee
15.30 - 15.55 Luis Filipe Vargas
Complexity Results About the Exactness of Sum-of-Squares Approximations for Polynomial Optimization
16.00 - 16.25 Mirte van der Eyden
Beyond free spectrahedra
16.30 - 16.55 Aljaz Zalar
A gap between positive even quartics and sums of squares ones

Tuesday, March 12th 2024
Room K503

9.00 - 9.45 Jan Stochel
Moment problem for discrete measures via idempotents
9.50 - 10.20 Matthias Schötz
Real Nullstellensatz for 2-step nilpotent Lie algebras
10.25 - 10.45 Coffee
10.45 - 11.10 Lorenzo Baldi
Carathéodory numbers and flat extension for measures supported on genus one curves
11.15 - 11.35 Clemens Brüser
Quadratic Determinantal Representations of Positive Polynomials
11.40 - 12.00 Lothar Sebastian Krapp
Schanuel's Conjecture, Roots of Exponential Polynomials and Peano Arithmetic

12.00 - 13.00 Lunch

13.00 - 17.00 Excursion to Hohentwiel (see also below)

Wednesday, March 13th 2024
Room K503

9.00 - 9.45 Jean-Bernard Lasserre
The Christoffel function: New applications, connections and extensions
9.50 - 10.20 Lucas Slot
Rational Christoffel functions for measures with conditional independence
10.25 - 10.45 Coffee
10.45 - 11.10 Rodolfo Ríos-Zertuche
Relaxation gaps for SDP-based algorithms for PDEs and optimal control
11.15 - 11.35 Tobias Metzlaff
Chebyshev Moments
11.40 - 12.00 Jared Miller
Maximizing Slice-Volumes of Semialgebraic Sets using Sum-of-Squares Programming

12.00 - 13.00 Lunch and Coffee

13.00 - 13.45 Hamza Fawzi
TBA
13.50 - 14.15 Shengding Sun
Generalizing determinantal inequalities using linear prinicipal minor (lpm) polynomials
14.20 - 14.45 Andreas Klingler
A homotopy method for convex optimization
14.50 - 15.10 Coffee
15.10 - 15.30 Carl Eggen
Granularity for mixed-integer polynomial optimization problems
15.35 - 15.55 David Sawall
Amalgamation of real zero polynomials with two common variables

16.00 - 24.00 Visiting Mainau and Conference Dinner (see also below)

Thursday, March 14th 2024
Room K503

9.00 - 9.45 Tim Netzer
Zeros of Polynomial Equations in Matrices, Quaternions and Beyond
9.50 - 10.20 Zenon Jablonski
Subnormality via moments
10.25 - 10.45 Coffee
10.45 - 11.10 Khazhgali Kozhasov
When are odd powers of non-negative forms SOS?
11.15 - 11.40 Alexander Taveira Blomenhofer
Nondefectivity of invariant secant varieties
11.45 - 12.05 Ivan Kovalyov
A truncated indefinite Stieltjes moment problem

12.05 - 13.00 Lunch and Coffee

13.00 - 13.30 Mateusz Michalek
Enumerative geometry meets statistics and optimization
13.35 - 14.00 Daniel Brosch
Combinatoric derivations in extremal graph theory and Sidorenko's conjecture
14.05 - 14.30 Hamza El Azhar
On the square root problem
14.35 - 14.55 Moritz Schick
Quantitative relation of the cones of sums of squares and sums of nonnegative circuit polynomials

15.00 - 15.30 Philipp di Dio and Tobias Sutter
Farewell and Coffee

Location & Venue

The conference is hosted at the University of Konstanz, Konstanz, Germany, in the rooms R0511 (Mon, Wed, Thu), L0602 (Tue), and K503 (Mon-Thu). See also the Maps of the University.

Train
Konstanz can be conveniently reached via train with the main train station (Konstanz Hauptbahnhof) being located in the city center. Searching and booking of connections can be done via the DB Navigator App of the German railway.

Air travel
The closest international airport to Konstanz is Zürich (Switzerland), with fast direct train connections (45min) to Konstanz main station. Other international airports are Stuttgart (3h), Frankfurt (4h), and Munich (5h).

Within Konstanz
Konstanz has a good public bus system, bus line 9 runs from the city center to the University every 15min. Tickets can be purchased online, at machines at the bus stations or directly in the bus. There are also various public bike and eScooter options available, which can be booked via the respective apps.

Registration & Application for Talks

We invite scholars from all career stages and backgrounds who are interested in the topic of the converence to participate.

Registration
To register, please email your details (name, institution, career stage) to the organizers MoPAT24@uni-konstanz.de by end of February.

Conference Fees
For the excursion and the dinner we have to charge a small fee since our funds can not support all participants:
- excursion: 20€ (entrance to Hohentwiel + transporation by bus)
- dinner: 40€ (entrance to the island of mainau + food + drinks)

You can bring your wife/husband/children to the conference dinner and the excursion. Adults pay the same fee as participants, for childen reduced fees are available.

How to pay the fee: TBA

Contributed Talks
Registered participants may contribute a talk to the conference. Please submit your title and abstract to MoPAT24@uni-konstanz.de by end of February.

Childcare
The University of Konstanz offers Childcare during events. We have limited funds to support childcare. Please let us know at least six weeks before the conference to organize.

Special Needs
If you have special needs, do not hesitate to contact us MoPAT24@uni-konstanz.de.

Official Letter of Registration/Participation from the Organizers
If you need (e.g. for visa purposes) an official confirmation letter of registration/participation for the conference we can provide this letter of participation/participation.

Hotel Recommendation

In Konstanz you can choose any hotel you like. We recommend the following hotels

  • ibis Konstanz: it is close to Sternplatz with easy access to bus lines to the university and the inner city, from Bahnhof (main station) take a bus to Sternplatz, from Sternplatz take bus 9A/B to Universität,
  • ibis budget Konstanz: take bus line 6 to/from Bahnhof (main station) or if you arrive with RE2 you can leave the train at Konstanz Fürstenberg and walk 750min/10min to this hotel; for the conference take bus 6 to Sternplatz and then 9A/B to Universtität,
  • harbr Hotel Konstanz

and youth hostel

  • Otto-Moericke-Tower Konstanz: 25min walking distance to the university, if you get a room in the tower you will have a beautiful view over the lake.

Tipp: The bus line 9A/B goes between Bahnhof (main station) and Universität (university). Bus line 13/4 and 4/13 between Bahnhof (main station) and Mainau (island). All these lines stop at Sternplatz next to the Rhein bridge.

Hohentwiel (by Philipp di Dio, 25th of August 2022)

Hohentwiel (by Philipp di Dio, 25th of August 2022)

Excursion

The excursion will take place on Tuesday, 12th of March 2024. We will visit the Hohentwiel Fortress Ruins with a beautiful view over the landscape. We plan to leave the University of Konstanz at 13.00 by bus and return at 17.00 from Hohentwiel.

The participation fee will be 20€ which includes entrance to Hohentwiel and transportation by bus from the University of Konstanz to Hohentwiel and back.

In case of bad weather forecast an alternative destination will be planned.


Island of Mainau (by Philipp di Dio, 18th of February 2023)

Island of Mainau (by Philipp di Dio, 28th of March 2023)

Conference Dinner

The conference dinner will take place Wednesday evening, 13th of March 2023, at the Island of Mainau at the Restaurant Comturey.

We plan to finish with the talks at approx. 16.00 to walk from the university to the island of Mainau (2km, 30min). A taxi can be organized going from the university to the island, so please let us know in advance if you can not walk this far.

The dinner will start at 18.00. The dinner fee will be 40€ which already includes the entrance fee to the island and drinks at the dinner. The island and the dinner venue will close for us at 24.00.

After the dinner the regular bus service can be used to go to the city/hotels.


Menu Conference Dinner

The dinner is organized as a buffet and the kitchen continuously prepares dishes.

Starters
carrot salad, cucumber salad, couscous salad, sweet pepper salad, leaf salad with Mainau herb dressing and balsamico dressing, different sorts of bread

Main courses
- thin strips of chicken with mushroom cream sauce
- pike-perch with dill cream sauce
- curry made with lentils (vegan)

Side dishes
butter rice, pasta, carrots, sweet pepper, zucchini

Desserts
mixed fruits, red fruit jelly with vanilla sauce

If you have any special dietary needs or allergies, please let us know in advance.

Island of Mainau (by Philipp di Dio, 28th of March 2023)

Funding



Sunrise over Lake Konstanz (by Philipp di Dio, 7th of February 2023, 7:25)

Why the name MoPAT?

See Moped.

What to visit in and around Konstanz?

 In Konstanz:

Ferry, ship, and boat tours on Lake Konstanz:

At and around Lake Konstanz (Bodensee):

FAQ

Can I bring my wife/husband/children to the conference (dinner, excursion)?
Yes. Additional adults pay the same fee as regular conference participants, for children we can offer reduced fees. For children the university provides childcare during events.

Island of Mainau (by Philipp di Dio, 22nd of April 2023)