T.B.A.
Donnerstag, 3.5.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
Homology of Lie algebras of generalized Jacobi matrices and its orthogonal, symplectic variants.
Montag, 7.5.18, 14:15-15:15, Hörsaal FRIAS, Albertstr. 19
In 1983, B. Feigin and B. Tsygan related the Homology of the\nLie algebra of generalized Jacobi matrices over a field k of\ncharacteristic 0. In this talk, I will explain my work with A. Fialowski on extension of their result to i) over any associative unital k-algebra R and ii) their orthogonal and symplectic subalgebras over R.
Topological field theory on r-spin surfaces and the Arf invariant
Montag, 7.5.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
We present a state-sum construction of TFTs on r-spin surfaces which uses a combinatorial model of r-spin structures. We give an example of such a TFT which computes the Arf invariant for r even. We use the combinatorial model and this TFT to calculate diffeomorphism classes of r-spin surfaces with parametrized boundary.
Hodge Numbers from Differential Equations
Montag, 7.5.18, 17:15-18:15, Raum 404, Ernst-Zermelo-Str. 1
A natural way of constructing Calabi-Yau manifolds is to build them as fibrations whose fibers are Calabi-Yau manifolds of lower dimension. For example, elliptic curves can be thought of as fibrations over the projective line by pairs of points, and K3 surfaces fibered over the projective line by elliptic curves form a large class of interesting K3 surfaces. In higher dimensions, the question of computing the Hodge numbers of such Calabi-Yau manifolds becomes a non-trivial one. I’ll talk about a method of computing Hodge numbers starting from the Picard-Fuchs differential equation of a family of Calabi-Yau manifolds. Applying this to families of lattice-polarized K3 surfaces provides a key ingredient in the classification of fibered Calabi-Yau threefolds.
Optimal Control of Thermoviscoplasticity
Dienstag, 8.5.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Elastoplastische Verformungen spielen eine wichtige Rolle in industriellen Verformungsprozessen. Oft finden diese unter nicht isothermen Bedingungen statt. Daher ist die Optimierung solcher Probleme nicht nur von mathematischem Interesse sondern insbesondere interessant für industrielle Anwendungen.\n\nIn meinem Vortrag werde ich die Analysis der Existenz von globalen Lösungen eines Optimalsteuerproblems basierend auf einem thermovisko(elasto)plastischen Modell und ihre Differenzierbarkeitseigenschaften diskutieren. Ich werde insbesondere auf die Schwierigkeiten eingehen, die durch die nichtlineare Koppelung der Wärmeleitungsgleichung mit den mechanischen Gleichungen des Models, entstehen.\n\nSchließlich werde ich einige numerische Beispiele präsentieren.
Verallgemeinerte Quantorenelemination und was nun?
Mittwoch, 9.5.18, 16:30-17:30, Raum 404, Ernst-Zermelo-Str. 1
Wir charakterisieren Klassen von (endlichen und unendlichen) Strukturen, die eine verallgemeinerte Quantorenelimination erlauben. Dabei erlaubt die Klasse K verallgemeinerte Quantorenelimination, wenn jede in der Logik der ersten Stufe definierbare Eigenschaft in K bereits durch eine Anzahl q von Quantoren ausgedrückt werden kann, die nur von K abhängt.\nFalls q = 0 gewählt werden kann, erhalten wir somit den \nklassischen Begriff der Quantorenelimination.\n
Some global analytic properties of VHS (…and of Hodge Modules)
Freitag, 11.5.18, 10:30-11:30, FRIAS
http://home.mathematik.uni-freiburg.de/gaav/index.html
Montag, 14.5.18, 00:00-01:00, Raum 226, Hermann-Herder-Str. 10
Gong Show: What I found on the arXiv
Montag, 14.5.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
The Paris-Harrington theorem
Mittwoch, 16.5.18, 16:30-17:30, Raum 404, Ernst-Zermelo-Str. 1
Let IRT, the infinite form of Ramsey's theorem, be the statement that for \(c\) a finite non-empty set and \n\(\bpi:[\bomega]^k \blongrightarrow c\) there is an infinite \(Y \bsubset \bomega\) with \(\bpi\) constant on \([Y]^k\). \nSuch an \(Y\) is called homogeneous for \(\bpi\). \n\nLet FRT, the finite form of Ramsey's theorem, be the statement that for \(c\) a finite non-empty set and \nevery positive \(m\) and \(k\) in \(\bomega\) there is an \(n \bin \bomega\) such that whenever \(X\) is a set of size \(n\) \nand \(\bpi: [X]^k \blongrightarrow c\) there is a set \(Y \bin [X]^m\) which is homogeneous for \(\bpi\). \n\nA (finite) subset \(Z\) of \(\bomega\) is called large if the size of \(Z\) is at least \(\bmin Z\). \n\nThe Paris-Harrington statement, PH, is FRT with the strengthened conclusion that the homogenous set \(Y\) \nmay be taken to be large. \n\n\n\nFRT may be deduced from IRT, as can PH; FRT may be proved in Peano arithmetic PA, thus without using the axiom \nof infinity; the remarkable result (1972, published 1977 in the Handbook of Mathematical Logic) of \nParis and Harrington is that PH is too strong to be provable in PA. \n\nThis talk will expound the work of many authors to show that PH fails in many non-standard models of PA. \n
Hyperbolicity of moduli spaces of CY
Donnerstag, 17.5.18, 10:30-11:30, Hörsaal FRIAS, Albertstr. 19
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
Mixed Hodge theory and representations of fundamental groups of algebraic varieties
Freitag, 18.5.18, 10:30-11:30, Hörsaal FRIAS, Albertstr. 19
TBA
Freitag, 18.5.18, 14:00-15:00, Hörsaal FRIAS, Albertstr. 19
On stable, closed geodesics on a K3
Montag, 28.5.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
I will report on the search for stable, closed geodesics on a K3 surface. In particular, I will sketch the Bourguignon-Yau proof of why the Riemann tensor vanishes along such geodesics, and I will explain how to find totally geodesic tori in highly symmetric Kummer K3s.
Iterated Ultrapowers in Set Theory
Mittwoch, 30.5.18, 16:05-17:05, Raum 404, Ernst-Zermelo-Str. 1
Given a measurable cardinal in an inner model of set theory we can\nconstruct its ultrapower, which is smaller than any of its factors.\nFollowing Kunen's work, we explain this process and its iteration.\n
Number Theory Day
Freitag, 1.6.18, 00:00-01:00, Basel