Sunrise over Lake Konstanz (Copyright Philipp di Dio)

Moments, Non-Negative Polynomials, and Algebraic Statistics

Winter School 2025, 17th - 21st February

Sun rise over Lake Konstanz (Copyright Philipp di Dio)

Winter School 2025, 17th - 21st February

Moments, Non-Negative Polynomials, and Algebraic Statistics

This winter school gives an introduction to moments, non-negative polynomials, and algebraic statistics for PhD students, postDocs, and interested Master students. Special topics are dealt with in more detail. The main topic is moments and their dual (non-negative polynomials). They are covered from a functional analytic point of view, a real-algebraic point of view, and an algebraic statistical point of view.

The winter school consists of lectures, exercise courses, special lectures, and small talks from participants. We welcome applications from participants for short talks about the presended and discussed topics.

Registration:
Write an email to the main organizer Philipp di Dio, see contact box on the right. If you need a letter of registration for the university administration or visa purposes please let us know.
Deadline for registration: 10th February 2025
Deadline for applications for short talks: 10th February 2025

Lecturers:

Philipp di Dio (Moments, Main Organizer)
Mario Kummer (Non-Negative Polynomials)
Carlos Amendola (Algebraic Statistics)

Special Lecturers:

Konrad Schmüdgen (to be confirmed)
Claus Scheiderer (confirmed)

About the Lecturers

Philipp di Dio (Moments, 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.

Mario Kummer (Non-Negative Polynomials)

Mario Kummer is a junior professor (tenure-track) for real algebraic geometry at the Technical University of Dresden.

His main research interest is real algebraic geometry.

Carlos Amendola (Algebraic Statistics)

Carlos Amendola is an assistant professor (tenure-track) of Algebraic and Geometric Methods in Data Analysis at the Institute of Mathematics of the Technical University of Berlin.

His main research interest is Algebraic Statistics. He is also very interested in developments concerning Applied Algebraic Geometry and Nonlinear Algebra.

List of Participants

Anh, Tran Hoang (National University of Singapore)
Amendola, Carlos (Technical University Berlin)
Baldi, Lorenzo (Max Planck Institute Leipzig)
Bauer, Mario (University of Konstanz)
Bechere, Matteo (University of Konstanz)
Brüser, Clemens (Technical University Dresden)
di Dio, Philipp (University of Konstanz)
Durasinovic, Srecko (Nanyang Technological University, Singapore)
González Nevado, Alejandro (University of Konstanz)
Kummer, Mario (Technical University Dresden)
Langer, Lars-Luca (University of Konstanz)
Pavlov, Dmitrii (Technical University Dresden)
Rieke, Nikolas (Technical University of Braunschweig)
Rodríguez, Joan Ferrer (University of Copenhagen)
Sawall, David (University of Konstanz)
Scheiderer, Claus (University of Konstanz)
Schmüdgen, Konrad (University of Leipzig, to be confirmed)
Telek, Máté (Max Planck Institute Leipzig)
Wirth, Laura (University of Konstanz)

Short List of Contents of the Lectures

Here you find a small overview of the content of the three main topics coverd by the winter school.

Moments

  • Moments, moment functionals, and their properties
  • Truncated moment functional and Richter's theorem
  • Adapted spaces
  • T-systems and sparse univariate Positivstellensätze
  • Positivity preservers

Non-Negative Polynomials

  • Cones of non-negative polynomials
  • Sums of squares
  • Non-negative polynomials on real algebraic varieties
  • Spectrahedral shadows

Algebraic Staticstics

  • TBA

Program & Schedule

Mon 17th of February - Fri 21st of February 2024

A detailed schedule of the winter school will follow.

Location & Venue

The winter school is hosted at the University of Konstanz, Konstanz, Germany, in room TBA. 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.

Hotel Recommendations

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.

What to visit in and around Konstanz?

 In Konstanz:

Ferry, ship, and boat tours on Lake Konstanz:

At and around Lake Konstanz (Bodensee):

Funding

Sunrise over Lake Konstanz (Copyright Philipp di Dio)