Das Mathematische Kolloquium ist eine gemeinsame wissenschaftliche Veranstaltung des gesamten Mathematischen Instituts. Es steht allen Interessierten offen und richtet sich neben den Mitgliedern und Mitarbeitern des Instituts auch an die Studierenden. Das Kolloquium findet dreimal im Semester am Donnerstag um 15:00 s.t. im Hörsaal II, Albertstr. 23b statt. Danach (gegen 16:15) gibt es Kaffee und Kekse, zu dem der vortragende Gast und alle Besucher eingeladen sind.
Habilitationsvortrag: Fast visualization of Mandelbrot and Julia sets
Donnerstag, 19.4.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Motivationsentwicklung im Mathematikstudium
Donnerstag, 26.4.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Der Übergang in ein Mathematikstudium wird oft problematisch erlebt.\nViele Studierende verlieren schnell ihre ursprünglich hohe intrinsische\nMotivation, ein hoher Anteil verlässt den Studiengang schon im ersten\nJahr wieder. Der Vortrag betrachtet diese Motivationsproblematik aus der\nPerspektive der Interesse-Forschung und der Selbstbestimmungstheorie der\nMotivation. In einer qualitativen Studie wurden 21 Studierende bis zu\ndrei Mal im ersten Studienjahr zu ihrem Studienerleben interviewt. Die\nAussagen erlauben eine genauere Beschreibung der Interessenentwicklung\nund des Erlebens der psychologischen Grundbedürfnisse. Die Ergebnisse\nzeigen vielfältige Gründe der Motivationsproblematik, insbesondere\nerklärt sich problematisches Autonomieerleben durch Schwierigkeiten der\nStudierenden mit dem selbstgesteuerten Arbeiten. Weiter werden\nVerbindungen zu den Besonderheiten der Hochschulmathematik und dem\nUnterschied zwischen Fach- und Gymnasiallehramtsstudierenden sichtbar.\n\n
Donnerstag, 26.4.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Universal Features of Price Formation in Financial Markets: Perspectives From Deep Learning
Donnerstag, 17.5.18, 17:00-18:00, HS Anatomiem (FRIAS), Albertstraße 17
\nUsing a large-scale Deep Learning approach applied to a high-frequency database containing billions of electronic market quotes and transactions for US equities, we uncover nonparametric evidence for the existence of a universal and stationary price formation mechanism relating the dynamics of supply and demand for a stock, as revealed through the order book, to subsequent variations in its market price. We assess the model by testing its out-of-sample predictions for the direction of price moves given the history of price and order flow, across a wide range of stocks and time periods. The universal price formation model is shown to exhibit a remarkably stable out-of-sample prediction accuracy across time, for a wide range of stocks from different sectors. Interestingly, these results also hold for stocks which are not part of the training sample, showing that the relations captured by the model are universal and not asset-specific.\nThe universal model --- trained on data from all stocks --- outperforms, in terms of out-of-sample prediction accuracy, asset-specific linear and nonlinear models trained on time series of any given stock, showing that the universal nature of price formation weighs in favour of pooling together financial data from various stocks, rather than designing asset or sector-specific models.
Ernst Zermelo, Freiburg, and Set Theory
Donnerstag, 17.5.18, 18:00-19:00, HS Anatomiem (FRIAS), Albertstraße 17
\nOn the occasion of the naming of Ernst-Zermelo-Strasse in Freiburg, Zermelo's fundamental and transformative\nwork in set theory is commemoratively brought to the fore in celebration.\nZermelo was an inventive mathematician who also worked throughout in applied mathematics, and we mention this well, in connection with several continuing uses of his name. The overall synopsis:\n\nZermelo made explicit the Axiom of Choice,\nand with it established the Well-Ordering Theorem, bringing in a pivotal proof that can be seen as a new technique in\nmathematics. Then he made explicit the now basic Zermelo axiomatization which initiated the current, abstract\nset theory. During his time in Freiburg, he initiated the current cumulative hierarchy view of set theory, which\nnow provides the basic heuristic for set theory with the iterative conception of set.\n\nIn concluding remarks, we briefly describe the vicissitudes of his last years in Freiburg both in set theory and at the Institute.\n
Donnerstag, 21.6.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Two-point functions in differential geometry and the Lawson conjecture
Donnerstag, 12.7.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
The Lawson conjecture from 1970 states the following:\n\nConjecture (Lawson, 1970). Any embedded minimal torus in the 3-dimensional unit-sphere is the Cliford torus.\n\n\n\nIn 2013, Brendle confirmed the validity of this conjecture thereby complementing the case of genus zero due to Almgren. Although Lawson himself provided many crucial ingredients used in the final proof by Brendle, the missing\npiece in the completion of the proof was finally given in form of a sophisticated use\nof the maximum principle on the surface T: Instead of trying to come up with an\nauxiliary function on T, an auxiliary function on the product T × T is constructed,\nwhich contains much more geometric information at points where a maximum is\nachieved. This method followed up similar techniques used earlier in the context of\nnon-collapsing for curvature flows by Andrews and Huisken. This auxiliary\nfunction led to the conclusion that the second fundamental form on T must have\nconstant length and due to an earlier result of Lawson, Brendle was able to conclude\nthat T must be the Clifford torus up to isometries.\nIn this talk we present this powerful method of two-point functions and sketch\nits various mentioned applications.
Donnerstag, 19.7.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
reserviert von Frau Mildenberger