Discrete Mathematics III Seminar: Algebra, Combinatorics, and Constructions

Winter 2015-16


Course Information

Topics and References

Seminar Schedule

Grading and Requirements




Tibor Szabó Codruţ Grosu Shagnik Das
Arnimallee 3, Rm 211a Arnimallee 3, Rm 207 Arnimallee 3, Rm 205
szabo at math dot fu-berlin dot de grosu.codrut at gmail dot com shagnnullik@mi.fu-bernulllin.de
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Course Information


A general prerequisite is familiarity with Combinatorics and Algebra (finite fields in particular).
A formal prerequisite is the successful completion of the Constructive Combinatorics (Discrete Mathematics III) course taught in Summer 2015, or consent of the instructor (please contact if necessary).


The course can be used as a Forschungsmodul or an Ergänzungsmodul in the Masters curriculum of the Freie Universität, or as an advanced seminar course in the curriculum of the Berlin Mathematical School.
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Topics and References

This seminar builds on the topics covered in the Constructive Combinatorics course, and focuses on recent advances in constructive combinatorics and related areas. While studying these topics, we shall explore connections to algebra and discrete geometry.

Below are a list of the talks that will be given, along with links to the source material.


Source material


No. of talks

Kakeya sets and joints Dvir; Kaplan-Sharir-Shustin Codrut 1
Random algebraic constructions Bukh; Conlon; Bukh-Conlon Shagnik/Tibor 2-3
Bipartite Turán numbers Ball-Pepe I; Ball-Pepe II Codrut 1-2
Bootstrap percolation in the hypercube Morrison-Noel-Scott; Morrison-Noel To be confirmed 1-2
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Seminar Schedule

Our seminar will meet on Mondays in Arnimallee 3 (rear building), SR 130, from 10:15 to 12:00, according to the schedule below.




2/11/2015 David Fabian Kakeya sets and joints
9/11/2015 Giulia Codenotti Random algebraic constructions I
16/11/2015 Giulia Codenotti/Jan Corsten Random algebraic constructions II
23/11/2015 Jan Corsten/Tomas Bayer Random algebraic constructions III
30/11/2015 Tomas Bayer Random algebraic constructions IV
7/12/2015 Ekaterina Oleynikova Bipartite Turán numbers I
14/12/2015 Ekaterina Oleynikova/Chris Kusch Bipartite Turán numbers II
25/1/2016 Chris Kusch Bipartite Turán numbers III
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Grading and Requirements


If you have partners for multiple talks on a topic, you should work together closely to understand your paper(s) and plan the individual talks.

Before the talks, you have to schedule at least two meetings with your adviser:
  • The first meeting should be at least two weeks before your scheduled talk. By this point, you should have read and worked through the paper(s) completely. The goal of this meeting is to clarify any parts of the material you do not fully understand. To this end, you should come prepared with concrete questions, such as, "How does line 45 follow from lines 23 and 38 in the proof of Theorem 3?" Simply saying, "I do not understand the proof of Theorem 3" is not acceptable.
  • The second meeting should be at least one week before your scheduled talk, and is practically a rehearsal. By this point, you should have your presentation completely prepared. If you are giving a Beamer presentation, all your slides should be completely finished - it is not okay to have any images or text missing. If you will be giving a blackboard presentation, you should have everything you plan to put on the board clearly written out, and notes on what you will be saying. The goal of this meeting is for the adviser to provide suggestions to improve the presentation ("This slide is too dense" or "Perhaps you should rearrange things here").
It is your responsibility to arrange the meetings with your adviser. Feel free to ask for extra meetings if you would like some additional input. If you miss or come unprepared to these meetings, or if your rehearsal fails to meet the minimum standards, your talk will be cancelled and you will not earn credit for the seminar.


You will be graded based on two criteria, both equally important:
  • your understanding of the topic, and
  • the quality of your presentation.
Successful completion of the seminar requires passing grades for both criteria.

Attendance and activity

To earn credit for the seminar, you must attend 90% of the lectures and pepper your colleagues with questions demanding clearer explanations of anything you do not understand in their talks. The goal of the seminar is not to allow the speaker to repeat his or her rehearsed talk in a calm and quiet setting, but rather that we the audience learn and appreciate some nice new mathematics. Bear in mind that it is the speaker who is there to serve the audience, and not vice versa!
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