Voraussetzungen: Analysis 1 (MA0001) und Lineare Algebra 1 (MA0004)
Inhalt: Es sollen interessante Ergebnisse aus der diskreten Mathematik besprochen werden. Zu den Themen gehören Färbungen, Kombinatorik, Graphentheorie, Netzwerke und Fehlererkennung.
Literatur: Sie finden die Bücher im Semesterapparat in der Bibliothek für Mathematik und Informatik.
A. Beutelspacher und M.-A. Zschiegner. Diskrete Mathematik für Einsteiger. Springer, 5. Auflage, 2014. Link zum e-book
Arthur Engel. Problem solving strategies. Springer, 1999.
Vortragseinteilung: Die ausfühlichen Vortragsthemen finden Sie hier.
Vortrag 1: Das Schubfachprinzip
Vortrag 2: Färbungsmethoden, Teil 1
Vortrag 3: Färbungsmethoden, Teil 2
Vortrag 4: Induktion
Vortrag 5: Zählen
Vortrag 6: Zahlentheorie
Vortrag 7: Fehlererkennung, Teil 1
Vortrag 8: Fehlererkennung, Teil 2
Vortrag 9: Graphentheorie, Teil 1
Vortrag 10: Graphentheorie, Teil 2
Vortrag 11: Netzwerke, Teil 1
Vortrag 12: Netzwerke, Teil 2
Vortrag 13: Boolsche Algebra
A list of previous courses can be found on TUMonline.
I supervise theses in the broad area of Probability Theory and Stochastic Processes. Please also have a look at my research interests.
If you are interested in writing a Bachelor or Master Thesis with me, please write me an email containing the approximative desired starting date, which courses in Stochastics you have taken, and what kind of topics would be interesting for you.
SInce I do not regularly offer seminars, having attended one of my seminars is not a requirement. However, for a Bachelor thesis with me you should have taken at least one of the Markov Chains [MA2404] or the Probability Theory [MA2409] courses. For a Master Thesis, Probability Theory [MA2409 or equivalent] is mandatory.
Research Interests
Probability Theory and Statistical Mechanics, in particular:
Gibbs measures and Gibbs point processes
Long-range order of discrete models in continuum, symmetry breaking, cristallization
Stochastic processes with long memory, Doeblin (g-)measures, partially odered models and their conceptional similarites with Gibbs measures
Hinweis: Die „Schnellsuche“ findet nur Text in den angezeigten
Feldern; nicht in Abstracts oder Schlagwörtern. Der Suchbegriff muss mindestens
3 Buchstaben lang sein.
2022
Conache, Diana; Heydenreich, Markus; Merkl, Franz; Rolles, Silke W. W.: Variance of voltages in a lattice Coulomb gas. J. Stat. Phys. 186 (1), 2022, Paper No. 16, 12 mehr…
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2019
Bauerschmidt, Roland; Conache, Diana; Heydenreich, Markus; Merkl, Franz; Rolles, Silke W. W.: Dislocation lines in three-dimensional solids at low temperature. Ann. Henri Poincaré 20 (9), 2019, 3019--3057 mehr…
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2018
Bethuelsen, Stein Andreas; Conache, Diana: One-Sided Continuity Properties for the Schonmann Projection. Journal of Statistical Physics 172 (4), 2018, 1147-1163 mehr…
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Conache, Diana; Daletskii, Alexei; Kondratiev, Yuri; Pasurek, Tanja: Gibbs states of continuum particle systems with unbounded spins: Existence and uniqueness. Journal of Mathematical Physics 59 (1), 2018, 013507 mehr…
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2015
Conache, Diana; Kondratiev, Yuri G.; Lytvynov, Eugene: Equilibrium Diffusion on the Cone of Discrete Radon Measures. Potential Analysis 44 (1), 2015, 71-90 mehr…
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2013
Putan, Diana; Stan, Diana: Dynamical behavior of endomorphisms on certain invariant sets. Mathematica Slovaca 63 (1), 2013, 135-142 mehr…
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Recent talks
Statistics Seminar, Bergen -- September 2023
Probability and geometry on configuration spaces, Berlin -- July 2023
GPSD Bochum -- February 2023
Conference of the Romanian Society of Probability and Statistics, Bucharest -- November 2022
GPSD Mannheim (online talk) -- September 2021
Probability Seminar, Queen Mary University, London -- October 2019
Statistics and Physics Seminar, Stavanger -- September 2019
Probability Seminar, Leiden -- September 2019
Oberseminar Wahrscheinlichkeitstheorie, LMU -- May 2019
Mini-Workshop: Mathematics of Crystallisation, Oberwolfach -- April 2019
