Winter School 2025 Moments

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.

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)

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

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

A detailed schedule of the winter school will follow.

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.

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.

 In Konstanz:

• Archäologisches Landesmuseum Baden-Württemberg: State archeological museum about Konstanz and the Lake Konstanz region, located at Sternplatz
• Konstanz city center with buildings from the middle ages (from 1380 and older)
• Konzil: the only time and place where a pope was elected in Germany
• Münster: Cathedral of Konstanz
• Sea Life: Aqua Marine Museum
• Therme: after a long day relax in the outdoor pool or in the sauna

Ferry, ship, and boat tours on Lake Konstanz:

• Bodensee Schifffahrt BSB: connecting several cities/harbors at Lake Konstanz
• Katamaran: a fast connection between Konstanz and Friedrichshafen
• ferry Konstanz/Staad - Meersburg: car, bike, and pedestrian ferry connecting Konstanz/Staad with Meersburg

At and around Lake Konstanz (Bodensee):

• Dornier Museum for Air and Space Flight: take the Katamaran from Konstanz habor to Friedrichshafen
• Hohentwiel: a old castle ruin on top of a vulcano
• Lindau Island: take a BSB boat from Konstanz harbor to Lindau
• Mainau Island: a flower island with beautiful gardens
• Meersburg: take bus 1 to Staad/Fähre and use the ferry
• München: take a FlixBus from Konstanz to Munich and visit e.g. one of the Pinakotheken (with one of van Gogh's sunflowers) or the Deutsches Museum (with the original desk and experimental setup of Otto Hahn and Fritz Straßmann for the first experimental proof of nuclear fission)
• Reichenau Island: famous for the landscape, the view, and several churches, especially Sankt Georg from the 9th century AD
• Rheinfall: take a train from Konstanz to Neuhausen Rheinfall
• Salem Monastery and Palace
• Straßburg: take a train from Konstanz to Straßburg
• Winterthur: take a train from Konstanz to Winterthur and visit e.g. the Kunst Museum
• Zurich: take a train from Konstanz to Zurich and visit e.g. the Kunsthaus or the Zoological Museum of the University Zurich