Mathematics

• Advanced Module: Differential Geometry III

  0280bA1.3
  • 19205201 Lecture
    Differential Geometry III (Konrad Polthier)
    Schedule: Di 12:00-14:00 (Class starts on: 2024-10-15)
    Location: T9/046 Seminarraum (Takustr. 9)
    

    Comments

    
    The lecture will introduce selected concepts from differential geometry and their role in solving current application problems.
    
    The topics include curvature measures, geometric flows, minimal surfaces, harmonic mapping, parallel transport, branched coverings, as well as their discretization and implementation.
    Practical problems come for example from the fields of geometric design, geometry processing, visualization, materials science, medicine, architecture.

    Prerequisites: Differential geometry I

  • 19205202 Practice seminar
    Practice seminar for Differential Geometry III (Tillmann Kleiner)
    Schedule: Fr 08:00-10:00 (Class starts on: 2024-10-18)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    The first tute will take place in semester week 2.

• Research Module: Differential Geometry

  0280bA1.4
  • 19214411 Seminar
    Research Module: Differential Geometrie (Konrad Polthier)
    Schedule: Di 14:00-16:00 (Class starts on: 2024-10-15)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    In this seminar, differential geometric topics will be independently developed based on current research and presented in the form of a talk.
    
    Particular emphasis is placed on the concrete implementation of differential geometric concepts in application scenarios and the questions of discretization and implementation.
    
    Learning objectives are a deeper understanding of differential geometry concepts, as well as problems and solution strategies in their practical use.
    
    Previous knowledge: Differential geometry I

• Introductory Module: Algebra I

  0280bA2.1
  • 19202501 Lecture
    Basic Module: Algebra I (Alexandru Constantinescu)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-14)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Content

    
    This is the first part of a three semester course on algebraic geometry. Commutative algebra is the theory of commutative rings and their modules. It formally includes affine algebraic and local analytic geometry. Topics include:

    ? Affine algebraic varieties

    ? Rings, ideals, and modules

    ? Noetherian rings

    ? Local rings and localization

    ? Primary decompositione

    ? Finite and integral extensions

    ? Dimension theory

    ? Regular rings

    Target Group
    Students with the prerequisites mentioned below.

    Prerequisites
    ? Linear Algebra I+II ? Algebra and Number Theory
    
    Literature
    ? Atiyah, M.F.; Macdonald, I.G.: Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969 ix+128 pp. (This book is probably the best entry to the subject. It is short, concise, and clearly written.)
    ? Further literature will be announced in class.

    
    Homepage: Professor Alexander Schmitt

  • 19202502 Practice seminar
    Practice seminar for Basic Module: Algebra I (Alexandru Constantinescu)
    Schedule: Mo 08:00-10:00 (Class starts on: 2024-10-21)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Advanced Module: Algebra III

  0280bA2.3
  • 19222301 Lecture
    Advanced Module: Algebra III (Alexander Schmitt)
    Schedule: Termine siehe LV-Details (Class starts on: 2024-10-16)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Comments

    Course contents: a selection of the following topics

    • properties of morphisms (proper, projective, smooth)
    • divisors
    • (quasi-)coherent sheaves
    • cohomology
    • Hilbert functions

    Suggested reading

    G.R. Kempf: Algebraic varieties. London Mathematical Society Lecture Note
    Series. 172. Cambridge: Cambridge University Press. 1993. x, 163 p.

    A. Schmitt: Homological algebra, lecture notes.

    J.L. Taylor: Several complex variables with connections to algebraic
    geometry and Lie groups. Graduate Studies in Mathematics. 46. Providence,
    RI: American Mathematical Society. 2002. xvi, 507 p.

  • 19222302 Practice seminar
    Practice seminar for Advanced Module: Algebra III (Jan Sevenster)
    Schedule: Mi 12:00-14:00 (Class starts on: 2024-10-16)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

• Research Module: Algebra

  0280bA2.4
  • 19214611 Seminar
    Reseach Module: Algebra (Alexander Schmitt)
    Schedule: Termine siehe LV-Details (Class starts on: 2024-10-15)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Target group:

    Math students

    Prerequisites

    Algebra I and II

    Homepage: Prof. Altmann

    Comments

    Contents:

    Seminar page

    Suggested reading

    Literatur

    Wird bekanntgegeben.

• Introductory Module: Discrete Mathematics II

  0280bA3.2
  • 19205801 Lecture
    Discrete Mathematics II - Algorithmic Comb. (Tibor Szabo)
    Schedule: Di 14:00-16:00, Do 14:00-16:00 (Class starts on: 2024-10-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Topics of the course

    • Algorithms and complexity (sorting, Dijkstra, TSP, approximation algorithms, matchings vs Hamiltonicity, P vs NP, certificates (Hall, Tutte), Hungarian algorithm, network flows and its applications (Menger, Baranyai), (list)-coloring, stable matching (Gale-Shapley Algorithm) and its application (Galvin))
    • Linear Programming (Simplex Algorithm), Duality and its applications in Combinatorics and Algorithms
    • Randomized algorithms (randomized matching algorithms, hypergraph-coloring, derandomization, Erdos-Selfridge Criterion, algorithmic Local Lemma)

     

    Suggested reading

    • L. Lovász, J. Pelikán, K. Vesztergombi, Discrete Mathematics
    • J. Matousek - B. Gaertner, Understanding and Using Linear Programming
    • D. West, Introduction to Graph Theory

    Further reading:

    • V. Chvátal, Linear Programming.
    • Schrijver, Theory of Linear and Integer Programming
    • Schrijver, Combinatorial Optimization

  • 19205802 Practice seminar
    Practice seminar for Discrete Mathematics II - Algorithmic Comb. (Tibor Szabo)
    Schedule: Di 12:00-14:00 (Class starts on: 2024-10-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Comments

    October 6th at 8:15-8:45 there will be an information question/answer opportunity about the rules and requirements of the course. (The first lecture starts at 9:00.)
    The first three weeks of the course will be given in a block course format during the week preceding the semester, October 6-10, hence there are no regular lectures during the period October 13-31. During the week of October 6-10 there will be lectures on four days, 9:15-12:00, about the fundamentals of Additive Combinatorics. These lectures will be accompanied by exercise sessions in the afternoon. In order to gain points towards their exercise credit, participants of Discrete Math II will be required to submit written solutions to some of these exercises during the first three weeks of the semester. The regular lecture and exercise hours will resume from November 3. For further details please check the course website: Discrete Mathematics II

• Introductory Module: Discrete Geometry I

  0280bA3.3
  • 19202001 Lecture
    Discrete Geometrie I (Georg Loho)
    Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2024-10-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

    Comments

    This is the first in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures including analysis and proof techniques. The material will be a selection of the following topics:
    Basic structures in discrete geometry

    • polyhedra and polyhedral complexes
    • configurations of points, hyperplanes, subspaces
    • Subdivisions and triangulations (including Delaunay and Voronoi)
    • Polytope theory
    • Representations and the theorem of Minkowski-Weyl
    • polarity, simple/simplicial polytopes, shellability
    • shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
    • graphs, diameters, Hirsch (ex-)conjecture
    • Geometry of linear programming
    • linear programs, simplex algorithm, LP-duality
    • Combinatorial geometry / Geometric combinatorics
    • Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
    • Arrangements, zonotopes, zonotopal tilings, oriented matroids
    • Examples, examples, examples
    • regular polytopes, centrally symmetric polytopes
    • extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
    • combinatorial optimization and 0/1-polytopes

     

    For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding for discrete-geometric structures appearing in differential geometry, topology, combinatorics, and algebraic geometry.

     

     

     

     

     

     

     

     

     

    Suggested reading

    • G.M. Ziegler "Lectures in Polytopes"
    • J. Matousek "Lectures on Discrete Geometry"
    • Further literature will be announced in class.

  • 19202002 Practice seminar
    Practice seminar for Discrete Geometrie I (Georg Loho)
    Schedule: Mo 16:00-18:00, Fr 10:00-12:00 (Class starts on: 2024-10-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

• Advanced Module: Discrete Geometry III

  0280bA3.6
  • 19205901 Lecture
    Advanced Module: Discrete Geometry III (Pavle Blagojevic)
    Schedule: Di 14:00-16:00 (Class starts on: 2024-10-15)
    Location: A7/SR 031 (Arnimallee 7)
    

    Additional information / Pre-requisites

    The target audience are students with a solid background in discrete geometry and/or convex geometry (en par with Discrete Geometry I & II). The topic of this course is a state-of-art of advanced topics in discrete geometry that find applications and incarnations in differential geometry, topology, combinatorics, and algebraic geometry.
    
    Requirements: Preferably Discrete Geometry I and II.

    Comments

    This is the third in a series of three courses on discrete geometry. This advanced course will cover a selection of the following topics (depending on the interests of the audience):   1. Oriented Matroids along the lines of the book Oriented Matroids by Björner, Las Vergnas, Sturmfels, White, and Ziegler; and/or   2. Triangulations along the lines of the book Triangulations by de Loera, Rambau, and Santos; and/or   3. Discriminants and tropical geometry along the lines of the book Discriminants, Resultants, and multidimensional determinants by Gelfand, Kapranov, and Zelevinsky; and/or   4. Combinatorics and commutative algebra along the lines of the book Combinatorics and commutative algebra by Stanley.

    Suggested reading

    Will be announced in class.

  • 19205902 Practice seminar
    Practice seminar for Advanced Module: Discrete Geometry III (Pavle Blagojevic)
    Schedule: Do 10:00-12:00 (Class starts on: 2024-10-17)
    Location: A3/SR 115 (Arnimallee 3-5)
    

• Research Module: Discrete Geometry

  0280bA3.8
  • 19206111 Seminar
    Research Module: Discrete Geometry (Giulia Codenotti)
    Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-16)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Pre-Meeting: see KVV

    Comments

    <p>This seminar will look at remarkable polytopes — among them regular polytopes, cyclic/neighborly polytopes, hypersimplices, 2simple-2simplicial polytopes, cut polytopes, etc. We discuss the examples, their construction and their most interesting properties. Some of these examples were designed or used in order to solve problems, refute conjectures, or to support conjectures. Some of these have unexplored or unexplainable properties, and those of course we want to look at as well.</p> <p>“It is not unusual that a single example or a very few shape an entire mathematical discipline. Examples are the Petersen graph, cyclic polytopes, the Fano plane, the prisoner dilemma, the real n-dimensional projective space and the group of two by two nonsingular matrices. And it seems that overall, we are short of examples. The methods for coming up with useful examples in mathematics (or counterexamples for commonly believed conjectures) are even less clear than the methods for proving mathematical statements.” — Gil Kalai (2000)</p>

    Suggested reading

    Themenvergabe und speziellere Literaturangaben in der Vorbesprechung zum Seminar.

• Introductory Module: Numerical Analysis II

  0280bA5.1
  • 19202101 Lecture
    Basic Module: Numeric II (Volker John)
    Schedule: Mo 10:00-12:00, Mo 14:00-20:00 (Class starts on: 2024-10-14)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    Description: Extending basic knowledge on initial value problems with ordinary differential equations from Numerik I, the course presents methods for stiff problems and multistep methods. In the second part of the course iterative methods for solving linear systems of equations are studied.

    Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

    Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

  • 19202102 Practice seminar
    Practice seminar for Basic Module: Numeric II (André-Alexander Zepernick)
    Schedule: Do 12:00-14:00 (Class starts on: 2024-10-17)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

• Advanced Module: Numerical Mathematics IV

  0280bA5.3
  • 19206401 Lecture
    Numerics IV: Modeling, Simulation, and Optimization (Christof Schütte)
    Schedule: Termine siehe LV-Details (Class starts on: 2024-10-18)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    Inhalt:

    Abstract:

    Modeling, Simulation, and Optimization (MSO) is one of the cornerstones of application-oriented mathematics.

    It covers a broad spectrum of research activities, ranging from the design of mathematical models for real-world processes, via efficient numerical simulation algorithms, to the solution of optimization problems for finding optimal scenarios or controls for the process under consideration. This lecture will give an overview over the techniques used in MSO and its application in different areas (life science, mobility, energy, sustainability, …). The lecture will be complemented by several pilot projects in which student groups will develop MSO solutions for realistic (but not too complex) application problems.

    Zielpublikum:
    Master Mathematik

    Suggested reading

    • Brokate and J. Sprekels: Hysteresis and Phase Transitions. Springer (1996)K.
    • Deckelnick, G. Dziuk, and Ch.M. Elliott: Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, p. 1-94 (2005)
    • G. Dziuk and Ch.M. Elliott: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, p. 262-292 (2007)
    • J.A. Sethian: Level Set Methods and Fast Marching Methods, CambridgeUniversity Press (1999)
    • T.J. Willmore: Riemannian Geometry, Clarendon, Oxford (1993)

  • 19206402 Practice seminar
    Practice seminar for Advanced Module: Numerics IV (Christof Schütte)
    Schedule: Di 10:00-12:00 (Class starts on: 2024-10-15)
    Location: A3/SR 115 (Arnimallee 3-5)
    

• Introductory Module: Differential Equations II

  0280bA6.2
  • 19242001 Lecture
    Partial Differential Equations II (Erica Ipocoana)
    Schedule: Di 08:00-10:00, Do 08:00-10:00 (Class starts on: 2024-10-15)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    Diese Veranstaltung baut auf dem Kursmaterial von Partielle Differentialgleichungen I des vorangegangenen Sommersemesters auf. Methoden für lineare partielle Differentialgleichungen werden vertieft und erweitert auf nichtlineare partielle Differentialgleichungen. Im Mittelpunkt der Vorlesung steht die Theorie monotoner und maximal monotoner Operatoren. 

    This course builds on the material of the course Partial Differential Equations I as taught in the previous summer term. Methods for linear partial differential equations will be deepened and extended to nonlinear partial differential equations. A central topic of the course is the theory of monotone and maximal monotone operators. 

  • 19242002 Practice seminar
    Tutorial Partial Differential Equations II (Erica Ipocoana)
    Schedule: Di 16:00-18:00 (Class starts on: 2024-10-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    

• Complementary Module: Selected Topics

  0280bA7.1
  • 19202501 Lecture
    Basic Module: Algebra I (Alexandru Constantinescu)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-14)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Content

    
    This is the first part of a three semester course on algebraic geometry. Commutative algebra is the theory of commutative rings and their modules. It formally includes affine algebraic and local analytic geometry. Topics include:

    ? Affine algebraic varieties

    ? Rings, ideals, and modules

    ? Noetherian rings

    ? Local rings and localization

    ? Primary decompositione

    ? Finite and integral extensions

    ? Dimension theory

    ? Regular rings

    Target Group
    Students with the prerequisites mentioned below.

    Prerequisites
    ? Linear Algebra I+II ? Algebra and Number Theory
    
    Literature
    ? Atiyah, M.F.; Macdonald, I.G.: Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969 ix+128 pp. (This book is probably the best entry to the subject. It is short, concise, and clearly written.)
    ? Further literature will be announced in class.

    
    Homepage: Professor Alexander Schmitt

  • 19205801 Lecture
    Discrete Mathematics II - Algorithmic Comb. (Tibor Szabo)
    Schedule: Di 14:00-16:00, Do 14:00-16:00 (Class starts on: 2024-10-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Topics of the course

    • Algorithms and complexity (sorting, Dijkstra, TSP, approximation algorithms, matchings vs Hamiltonicity, P vs NP, certificates (Hall, Tutte), Hungarian algorithm, network flows and its applications (Menger, Baranyai), (list)-coloring, stable matching (Gale-Shapley Algorithm) and its application (Galvin))
    • Linear Programming (Simplex Algorithm), Duality and its applications in Combinatorics and Algorithms
    • Randomized algorithms (randomized matching algorithms, hypergraph-coloring, derandomization, Erdos-Selfridge Criterion, algorithmic Local Lemma)

     

    Suggested reading

    • L. Lovász, J. Pelikán, K. Vesztergombi, Discrete Mathematics
    • J. Matousek - B. Gaertner, Understanding and Using Linear Programming
    • D. West, Introduction to Graph Theory

    Further reading:

    • V. Chvátal, Linear Programming.
    • Schrijver, Theory of Linear and Integer Programming
    • Schrijver, Combinatorial Optimization

  • 19208001 Lecture
    Probability Theory III (Nicolas Perkowski, N.N.)
    Schedule: Mi 08:00-10:00, Do 10:00-12:00 (Class starts on: 2024-10-16)
    Location: T9/046 Seminarraum (Takustr. 9)
    

    Comments

    Stochastic analysis is the study of stochastic processes that evolve in continuous time. We will treat the following subjects, among others:

    Gaussian processes; Brownian motion, construction and properties; filtrations and stopping times; continuous time martingales; continuous semimartingales; quadratic variation; stochastic integration; Itô’s formula; Girsanov’s theorem and change of measure; time change; martingale representation; stochastic differential equations and diffusion processes, connections with partial differential equations.

    Detailed Information can be found on the Homepage of 19208001 Stochastics III.

  • 19225101 Lecture
    Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation (Luigi Delle Site)
    Schedule: Mo 12:00-14:00, Di 12:00-14:00 (Class starts on: 2024-10-14)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Audience: Master students of Mathematics and Physics interested in mathematical theory and computational modeling of Soft Matter Systems.

    Requirements: Basic Knowledge of statistical physics and of dynamics, computer programming

    Comments

    Program

    Polymer Physics: Structure and Dynamics

    • (a) Theoretical/analytic approaches
    • (b) Physical and chemical Modeling
    • (c) Simulation

    Biological Membranes

    • (a) Theoretical/analytic approaches
    • (b) Physical and chemical Modeling
    • (c) Simulation

    Introduction to Colloids and Liquid Crystals

    • Theory and Simulation

    Introduction to Hydrodynamic scale for large Biological Systems:

    • Examples are e.g. Cellular processes, Red Blood Cells in Capillary Flow, etc. (Theory and Simulation)

    Suggested reading

    Basic Literature:

    1. Introduction to Polymer Physics by M. Doi
    2. Soft Matter Physics by M. Doi
    3. Biomembrane Frontiers: Nanostructures, Models, and the Design of Life (Handbook of Modern Biophysics) by von Thomas Jue, Subhash H. Risbud, Marjorie L. Longo, Roland Faller (Editors)

  • 19303601 Lecture
    Cryptography and Security in Distributed Systems (Volker Roth)
    Schedule: Mi 14:00-16:00, Do 12:00-14:00 (Class starts on: 2024-10-16)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Requirements: Participants must have a good mathematical understanding and good knowledge of computer security and networking.

    Comments

    This course gives an introduction to cryptography and cryptographic key management, as well as an introduction to cryptographic protocols and their application in the field of security in distributed systems. Relevant mathematical tools will be developed accordingly. In addition, the lecture addresses the importance of implementation details in the context of IT system security.

    Suggested reading

    • Jonathan Katz and Yehuda Lindell, Introduction to Modern Cryptography, 2008
    • Lindsay N. Childs, A Concrete Introduction to Higher Algebra. Springer Verlag, 1995.
    • Johannes Buchmann, Einfuehrung in die Kryptographie. Springer Verlag, 1999.

    Weitere noch zu bestimmende Literatur und Primärquellen.

  • 19202502 Practice seminar
    Practice seminar for Basic Module: Algebra I (Alexandru Constantinescu)
    Schedule: Mo 08:00-10:00 (Class starts on: 2024-10-21)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    
  • 19205802 Practice seminar
    Practice seminar for Discrete Mathematics II - Algorithmic Comb. (Tibor Szabo)
    Schedule: Di 12:00-14:00 (Class starts on: 2024-10-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Comments

    October 6th at 8:15-8:45 there will be an information question/answer opportunity about the rules and requirements of the course. (The first lecture starts at 9:00.)
    The first three weeks of the course will be given in a block course format during the week preceding the semester, October 6-10, hence there are no regular lectures during the period October 13-31. During the week of October 6-10 there will be lectures on four days, 9:15-12:00, about the fundamentals of Additive Combinatorics. These lectures will be accompanied by exercise sessions in the afternoon. In order to gain points towards their exercise credit, participants of Discrete Math II will be required to submit written solutions to some of these exercises during the first three weeks of the semester. The regular lecture and exercise hours will resume from November 3. For further details please check the course website: Discrete Mathematics II

  • 19208002 Practice seminar
    Tutorial: Probability Theory III (N.N.)
    Schedule: Do 16:00-18:00 (Class starts on: 2024-10-17)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    
  • 19225102 Practice seminar
    Practice seminar for Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation (Luigi Delle Site)
    Schedule: Mi 12:00-14:00 (Class starts on: 2024-10-16)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    
  • 19303602 Practice seminar
    Practice seminar for Cryptography and Security in Distributed Systems (Volker Roth)
    Schedule: Do 14:00-16:00 (Class starts on: 2024-10-17)
    Location: T9/SR 006 Seminarraum (Takustr. 9)
    

• Complementary Module: Selected Research Topics

  0280bA7.2
  • 19235701 Lecture
    Introduction to mathematical modeling with partial differential equations (Marita Thomas)
    Schedule: Di 10:00-12:00 (Class starts on: 2024-10-15)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    The course gives an introduction to mathematical modeling with partial differential equations. It discusses a selection of the following topics:  

    • General principles of continuum mechanics and thermodynamics

    • Symmetries and conservation laws

    • Variational principles

    • Derivation and discussion of models from hydrodynamics, solid mechanics, thermoelasticity, geodynamics, climate research or quantum mechanics

    This course can be attended as the first part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered in the subsequent summer term by the course 19215301 + 19215302 "Mathematical Modelling in Climate Research". 

     

  • 19320501 Lecture
    Quantum Cryptanalysis (Marian Margraf)
    Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2024-10-15)
    Location: T9/SR 006 Seminarraum (Takustr. 9)
    

    Comments

    The lecture aims at a deeper understanding of cryptographic algorithms, especially which design criteria have to be considered for the development of secure encryption algorithms. For that purpose we will get to know and evaluate different cryptanalytic methods for symmetrical and asymmetrical encryption techniques – e.g. linear and differential cryptanalysis on block ciphers, correlation attacks on stream ciphers and algorithms to solve the factorization problem and the discrete logarithm problem. Weaknesses in the implementation, e.g. to exploit side-channel attacks, will be discussed only peripherally.

  • 19320502 Practice seminar
    Practice seminar for Cryptanalysis (Marian Margraf)
    Schedule: -
    Location: keine Angabe
    

• Complementary Module: Specific Aspects

  0280bA7.3
  • 19235701 Lecture
    Introduction to mathematical modeling with partial differential equations (Marita Thomas)
    Schedule: Di 10:00-12:00 (Class starts on: 2024-10-15)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    The course gives an introduction to mathematical modeling with partial differential equations. It discusses a selection of the following topics:  

    • General principles of continuum mechanics and thermodynamics

    • Symmetries and conservation laws

    • Variational principles

    • Derivation and discussion of models from hydrodynamics, solid mechanics, thermoelasticity, geodynamics, climate research or quantum mechanics

    This course can be attended as the first part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered in the subsequent summer term by the course 19215301 + 19215302 "Mathematical Modelling in Climate Research". 

     

  • 19235702 Practice seminar
    Introduction to mathematical modeling with partial differential equations (Marita Thomas)
    Schedule: Di 14:00-16:00 (Class starts on: 2024-10-15)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

• Complementary Module: Specific Research Aspects

  0280bA7.4
  • 19234201 Lecture
    Topology and Topoi (Georg Lehner)
    Schedule: Mo 10:00-12:00 (Class starts on: 2024-10-14)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    There are various dualities in mathematics that share formal similarities. One is given by Galois theory: For a given field, the poset of Galois extensions and the poset of subgroups of its absolute Galois group are dual to another. Another example is covering space theory: For a given topological space, there is a duality between coverings and subgroups of its fundamental group. We will also discuss Stone dualities, as well as various incarnations of these.

    These dualities are special cases of a very general phenomenon that can be expressed by looking at Grothendieck Topoi. These Topoi are categories of sheaves on a site, and can also be thought of as generalized topological spaces. Any topos has a pro-finite homotopy group and there is an abstract Galois theory that generalizes both classical Galois theory and covering space theory.

    Towards the end of the lecture series we will look at shape theory. Shape theory allows one to do homotopy theory even with wild topological spaces. To any higher topos, one can associate its shape. We will attempt to prove the result that for a locally contractible topos, its sub-topos of locally contractible objects is equivalent to the category of local systems over its shape.

    Suggested reading

    Johnstone - Stone Spaces
    MacLane, Moerdijk - Sheaves in Geometry and Logic
    Hoyois - Higher Galois Theory

  • 19244901 Lecture
    Special seminar in numerical analysis/stochastics (Ana Djurdjevac)
    Schedule: Mi 16:00-18:00 (Class starts on: 2024-10-16)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    Content:

    This seminar is at the interface of  stochastic differential equations and numerical analysis. The seminar will be held as a block course. In the first four weeks there will be four lectures explaining basics of the topics specified bellow. At the beginning of the semester, students will be given papers with particular methods related to those topics that they should work on and implement by the end of the semester. In the last weeks of the semester,  students will  give presentations in which the project results will be presented and they will also submit short report about their topic.

    The seminar will cover a selection from the following topics:

    • Full discretization of parabolic PDEs
    • Numerical methods for SDEs, such as Euler-Maruyama Method, Milstein Method, exponential integrators
    • Weak and strong convergence
    • Galerkin methods for semilinear stochastic PDEs
    • Monte-Carlo and Multilevel Monte-Carlo sampling methods

    Target audience: 

    M.Sc. Mathematik/Physik, BMS course

    Requirements:

    Stochastic I and Numerics II.  Basic knowledge from measure theory, functional analysis and numerical analysis.

    Suggested reading

    Suggested reading:

    [1] T. J. Sullivan. Introduction to Uncertainty Quantification, volume 63 of Texts in Applied Mathematics. Springer, 2015.

    [2] Lord, Gabriel J., Catherine E. Powell, and Tony Shardlow. An Introduction to computational stochastic PDEs. Vol. 50. Cambridge University Press, 2014.

    [3]  P. E. Kloeden, E. Platen. Numerical Solution of Stochastic Differential Equations. Springer 1992

    [4] V. Thomee. Galerkin Finite Element Methods for Parabolic Problems. Springer 2006

• Complementary Module: Research Seminar

  0280bA7.5
  • 19206111 Seminar
    Research Module: Discrete Geometry (Giulia Codenotti)
    Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-16)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Pre-Meeting: see KVV

    Comments

    <p>This seminar will look at remarkable polytopes — among them regular polytopes, cyclic/neighborly polytopes, hypersimplices, 2simple-2simplicial polytopes, cut polytopes, etc. We discuss the examples, their construction and their most interesting properties. Some of these examples were designed or used in order to solve problems, refute conjectures, or to support conjectures. Some of these have unexplored or unexplainable properties, and those of course we want to look at as well.</p> <p>“It is not unusual that a single example or a very few shape an entire mathematical discipline. Examples are the Petersen graph, cyclic polytopes, the Fano plane, the prisoner dilemma, the real n-dimensional projective space and the group of two by two nonsingular matrices. And it seems that overall, we are short of examples. The methods for coming up with useful examples in mathematics (or counterexamples for commonly believed conjectures) are even less clear than the methods for proving mathematical statements.” — Gil Kalai (2000)</p>

    Suggested reading

    Themenvergabe und speziellere Literaturangaben in der Vorbesprechung zum Seminar.

  • 19214411 Seminar
    Research Module: Differential Geometrie (Konrad Polthier)
    Schedule: Di 14:00-16:00 (Class starts on: 2024-10-15)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    In this seminar, differential geometric topics will be independently developed based on current research and presented in the form of a talk.
    
    Particular emphasis is placed on the concrete implementation of differential geometric concepts in application scenarios and the questions of discretization and implementation.
    
    Learning objectives are a deeper understanding of differential geometry concepts, as well as problems and solution strategies in their practical use.
    
    Previous knowledge: Differential geometry I

  • 19214611 Seminar
    Reseach Module: Algebra (Alexander Schmitt)
    Schedule: Termine siehe LV-Details (Class starts on: 2024-10-15)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Target group:

    Math students

    Prerequisites

    Algebra I and II

    Homepage: Prof. Altmann

    Comments

    Contents:

    Seminar page

    Suggested reading

    Literatur

    Wird bekanntgegeben.

  • 19226511 Seminar
    Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
    Schedule: Fr 12:00-14:00 (Class starts on: 2024-10-18)
    Location: A7/SR 031 (Arnimallee 7)
    

    Additional information / Pre-requisites

    Audience: At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

    Comments

    Content: The seminar will concern the discussion of state-of-art techniques in molecular simulation which allow for a simulation of several space (especially) and time scale within one computational approach.

    The discussion will concerns both, specific computational coding and conceptual developments.

    Suggested reading

    Related Basic Literature:

    (1) M.Praprotnik, L.Delle Site and K.Kremer, Ann.Rev.Phys.Chem.59, 545-571 (2008)

    (2) C.Peter, L.Delle Site and K.Kremer, Soft Matter 4, 859-869 (2008).

    (3) M.Praprotnik and L.Delle Site, in "Biomolecular Simulations: Methods and Protocols" L.Monticelli and E.Salonen Eds. Vol.924, 567-583 (2012) Methods Mol. Biol. Springer-Science

  • 19229917 Seminar / Undergraduate Course
    KI als Werkzeug in der Mathematik (Georg Loho)
    Schedule: Di 16:00-18:00 (Class starts on: 2024-10-15)
    Location: A7/SR 031 (Arnimallee 7)
    

    Comments

    Je nach Bedarf: 

    "KI als Werkzeug in der Mathematik" oder "Geometrie & Optimierung" oder etwas wie "Spieltheorie & Gesellschaft"

    Suggested reading

    G. D. James "The representation theory of the symmetric group" Springer, Lecture Notes in Mathemtaics vol 682, 1978

    B. E. Sagan "The Symmetric Group - Representations, Combinatorial Algorithms, and Symmetric Functions" 2nd Edition, 2000

  • 19239711 Seminar
    Infinite-Dimensional Dynamics (Bernold Fiedler, Isabelle Schneider)
    Schedule: Do 16:00-18:00 (Class starts on: 2024-10-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in delay equations.

  • 19239911 Seminar
    Nonlinear Dynamics (Bernold Fiedler, Isabelle Schneider)
    Schedule: Do 14:00-16:00 (Class starts on: 2024-10-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in dynamical systems.

• Complementary Module: BMS Fridays

  0280bA7.8
  • 19223111 Seminar
    BMS Fridays (Holger Reich)
    Schedule: Fr 14:00-17:00 (Class starts on: 2024-10-25)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    The Friday colloquia of BMS represent a common meeting point for Berlin mathematics at Urania Berlin: a colloquium with broad emanation that permits an overview of large-scale connections and insights. In thematic series, the conversation is about “mathematics as a whole,” and we hope to be able to witness some breakthroughs.

    Typically, there is a BMS colloquium every other Friday afternoon in the BMS Loft at Urania during term time. BMS Friday colloquia usually start at 2:15 pm. Tea and cookies are served before each talk at 1:00 pm.

    More details: https://www.math-berlin.de/academics/bms-fridays

• Complementary Module: What is…?

  0280bA7.9
  • 19217311 Seminar
    PhD Seminar "What is...?" (Holger Reich)
    Schedule: Fr 12:00-14:00 (Class starts on: 2024-10-18)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    The "What is ...?" seminars are usually held before the BMS Friday seminar to complement the topic of the talk.

    Audience: Anybody interested in mathematics is invited to attend the "What is ...?" seminars. This includes Bachelors, Masters, Diplom, and PhD students from any field, as well as researchers like Post-Docs.
    Requirements: The speakers assume that the audience has at least a general knowledge of graduate-level mathematics.

    Comments

    Content: The "What is ...?" seminar is a 30-minute weekly seminar that concisely introduces terms and ideas that are fundamental to certain fields of mathematics but may not be familiar in others.
    The vast mathematical landscape in Berlin welcomes mathematicians with diverse backgrounds to work side by side, yet their paths often only cross within their individual research groups. To encourage interdisciplinary cooperation and collaboration, the "What is ...?" seminar attempts to initiate contact by introducing essential vocabulary and foundational concepts of the numerous fields represented in Berlin. The casual atmosphere of the seminar invites the audience to ask many questions and the speakers to experiment with their presentation styles.
    The location of the seminar rotates among the Urania, FU, TU, and HU. On the weeks when a BMS Friday takes place, the "What is ...?" seminar topic is arranged to coincide with the Friday talk acting as an introductory talk for the BMS Friday Colloquium. For a schedule of the talks and their locations, check the website. The website is updated frequently throughout the semester.

    Talks and more detailed information can be found here
    Homepage: http://www.math.fu-berlin.de/w/Math/WhatIsSeminar

• Modules w/o courses in this semester

  19 Modules
  • Introductory Module: Differential Geometry I 0280bA1.1
  • Introductory Module: Differential Geometry II 0280bA1.2
  • Introductory Module: Algebra II 0280bA2.2
  • Introductory Module: Discrete Mathematics I 0280bA3.1
  • Introductory Module: Discrete Geometry II 0280bA3.4
  • Advanced Module: Discrete Mathematics III 0280bA3.5
  • Research Module: Discrete Mathematics 0280bA3.7
  • Introductory Module: Topology I 0280bA4.1
  • Introductory Module: Topology II 0280bA4.2
  • Introductory Module: Visualization 0280bA4.3
  • Advanced Module: Topology III 0280bA4.4
  • Research Module: Topology 0280bA4.5
  • Introductory Module: Numerical Analysis III 0280bA5.2
  • Research Module: Numerical Mathematics 0280bA5.4
  • Introductory Module: Differential Equations I 0280bA6.1
  • Advanced Module: Differential Equations III 0280bA6.3
  • Research Module: Applied Analysis and Differential Equations 0280bA6.4
  • Complementary Module: Research Project 0280bA7.6
  • Complementary Module: Probability and Statistics II 0280bA7.7