Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Annette Huber-Klawitter, Amador Martín Pizarro
Assistant: Christoph Brackenhofer
Language: in German
Semi-algebraic geometry is about properties of subsets of \(**R**^n\), which are given by inequalities of the form [ f(x1, \dots, xn)\geq 0] for polynomials \(f\in**R**[X_1,\dots,X_n]\).
The theory has many different facets. On the one hand, it can be seen as a version of algebraic geometry over \(\mathbf{R}\) (or even more generally over so-called real closed fields). On the other hand, the properties of these fields are a central tool for the model-theoretic proof of Tarski-Seidenberg's theorem on quantifier elimination in real closed fields. Geometrically, this is interpreted as a projection theorem.
From this theorem, a proof of Hilbert's 17th problem easily follows, which was solved by Artin in 1926.
\textit{Is every real polynomial \(P \in \mathbf{R}[x_1, \dots, x_n]\), which takes a non-negative value for every \(n\)-tuple in \(\mathbf{R}^n\), a sum of squares of rational functions (i.e., quotients of polynomials)?}
In the lecture, we will explore both aspects. Necessary tools from commutative algebra or model theory will be discussed according to the prior knowledge of the audience.
Required: Algebra and Number Theory \ Recommended: Knowledge in commutative algebra and algebraic geometry (cf. Kommutative Algebra und Einführung in die algebraische Geometrie), model theory
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Seminar: Fr, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary Meeting 15.07., 11:00, SR 318, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Annette Huber-Klawitter
Assistant: Xier Ren
Language: Talk/participation possible in German and English
In this seminar, we are going to study finite dimensional (unital, possibly non-commutative) algebras over a (commutative) field \(k\). Prototypes are the rings of square matrices over \(k\), finite field extensions, or the algebra \(k^n\) with diagonal multiplication.
We will concentrate on path algebras of finite quivers (German: Köcher). Modules over them are equivalently described as representations of the quiver. Many algebraic properties can be directly understood from properties of the quiver.
Required: Linear Algebra \ Recommended: Algebra and Number Theory, Commutative Algebra and Introduction to Algebraic Geometry
Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
oram exam (resit) 04.12., 00:00-00:00
Teacher: Annette Huber-Klawitter
Assistant: Christoph Brackenhofer
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter
Do, 14-15h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Markus Junker, Amador Martín Pizarro
Teacher: Annette Huber-Klawitter
Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
29.01., 08:00-00:00
Teacher: Annette Huber-Klawitter
Assistant: Andreas Demleitner
general:
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Di, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter
Assistant: Christoph Brackenhofer
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Do, 14-15h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Markus Junker, Amador Martín Pizarro
Teacher: Annette Huber-Klawitter
Assistant: Pedro Núñez
general: ,
Compulsory Elective in Mathematics (BSc21)
Elementary Geometry (2HfB21, MEH21, MEB21, MEdual24)
Lecture: Di, Do, 8-10h, HS Rundbau, Albertstr. 21
Teacher: Annette Huber-Klawitter
Assistant: Christoph Brackenhofer, Pedro Núñez
general: ,
Linear Algebra II (BScInfo19, BScPhys20)
Di, 10-12h, SR 125, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter
Fr, 10-12h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Do, 14-15h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Markus Junker, Amador Martín Pizarro
Lecture: Mo, Do, 8-10h, HS Rundbau, Albertstr. 21
27.02., 13:00-17:00
Teacher: Annette Huber-Klawitter
Assistant: Vivien Vogelmann
general: ,
Linear Algebra I (BScInfo19, BScPhys20)
Di, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter
Assistant: Luca Terenzi
general:
Compulsory Elective in Mathematics (BSc21)
Fr, 10-12h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Lecture: Fr, 8-10h, HS Weismann-Haus, Albertstr. 21a
02.08., 13:00-16:00
Sit-in exam (resit) 16.09., 09:00-13:00
Teacher: Annette Huber-Klawitter
Assistant: Pedro Núñez
general: ,
Compulsory Elective in Mathematics (BSc21)
Elementary Geometry (2HfB21, MEH21, MEB21, MEdual24)
Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
26.07., 10:00-13:00
Sit-in exam (resit) 07.10., 08:30-11:00
Teacher: Annette Huber-Klawitter
Assistant: Luca Terenzi
general:
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Fr, 10-12h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Sebastian Goette, Nadine Große, Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Assistant: Vivien Vogelmann
Lecture: Mo, Mi, 10-12h, HS Weismann-Haus, Albertstr. 21a
16.02., 13:00-17:00
Sit-in exam (resit) 30.05., 13:30-16:30
Teacher: Annette Huber-Klawitter
Assistant: Pedro Núñez
general: ,
Algebra and Number Theory (2HfB21, MEH21)
Compulsory Elective in Mathematics (BSc21)
Introduction to Algebra and Number Theory (MEB21)
Pure Mathematics (MSc14)
Do, 8-10h, SR 125, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter
Assistant: Luca Terenzi
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mi, 14-16h, HS II, Albertstr. 23b
Teacher: Sebastian Goette, Nadine Große, Annette Huber-Klawitter, Stefan Kebekus
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter, Stefan Kebekus
Fr, 8-10h, , online
29.07., 09:00-13:00
Teacher: Annette Huber-Klawitter
Assistant: Lukas Braun
general: ,
Compulsory Elective in Mathematics (BSc21)
Elementary Geometry (2HfB21, MEH21, MEB21, MEdual24)
Mi, 8-10h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter
Assistant: Lukas Braun
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Fr, 10-12h, bbb-Raum "Anderssen", online
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Mi Do, 14-16h, bbb-Raum des Graduiertenkollegs, online
Teacher: Andriy Haydys, Annette Huber-Klawitter, Fritz Hörmann, Stefan Kebekus, Sebastian Goette, Nadine Große, Wolfgang Soergel, Katrin Wendland
Assistant: Jonas Schnitzer
Lecture: Di, Do, 8-10h, bbb-Raum "Sprechstunde Prof. Huber-Klawitter", online
Teacher: Annette Huber-Klawitter
general:
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Mo, 14-16h, bbb-Raum "Sprechstunde Prof. Huber-Klawitter", online
Teacher: Annette Huber-Klawitter
Assistant: Lukas Braun
Supplementary Module in Mathematics (MEd18)
Compulsory Elective in Mathematics (BSc21)
Mi 14-16h, SR 125, Ernst-Zermelo-Str. 1, Do, 14-16h, bbb-Raum "Krush", online
Teacher: Nadine Große, Andriy Haydys, Annette Huber-Klawitter, Wolfgang Soergel, Stefan Kebekus, Katrin Wendland
Fr, 10-12h, , online
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Lecture: Di, Do, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Bradley Drew, Annette Huber-Klawitter
Assistant: Johan Commelin
general:
Compulsory Elective in Mathematics (BSc21)
Mi, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter
Assistant: Lukas Braun
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Mi, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Sebastian Goette, Nadine Große, Andriy Haydys, Annette Huber-Klawitter, Wolfgang Soergel, Katrin Wendland, Stefan Kebekus
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Lecture: Di, Do, 8-10h, HS Rundbau, Albertstr. 21
17.09., 08:00-12:00
Sit-in exam (resit) 02.12., 14:00-18:00
Teacher: Annette Huber-Klawitter
Assistant: Johan Commelin
general: , ,
Linear Algebra II (BScInfo19, BScPhys20)
Mi, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter
Assistant: Johan Commelin
Compulsory Elective in Mathematics (BSc21)
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter, Wolfgang Soergel
Mi 14-16h, SR 404, Ernst-Zermelo-Str. 1, Di, 12-14h, SR 218, Ernst-Zermelo-Str. 1
Teacher: Sebastian Goette, Nadine Große, Annette Huber-Klawitter, Andriy Haydys, Wolfgang Soergel, Katrin Wendland
Lecture: Mo, Do, 8-10h, HS Rundbau, Albertstr. 21
08.03., 15:00-18:00
Sit-in exam (resit) 04.07., 12:30-15:30
Teacher: Annette Huber-Klawitter
Assistant: Fritz Hörmann, Leonardo Patimo
general: , ,
Mo, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter
Assistant: Oliver Bräunling
Supplementary Module in Mathematics (MEd18)
Compulsory Elective in Mathematics (BSc21)
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Mi, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Sebastian Goette, Nadine Große, Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel, Katrin Wendland, Andriy Haydys, Fritz Hörmann