current teaching


University of Vienna:

2019 Summer: Modern techniques in combinatorial set theory.

What original ideas lead to the breakthrough results of infinite combinatorics in the last 30 years? Which methods found the widest range of applications? The main purpose of this course is to overview novel techniques from the theory of (mostly) discrete structures of small uncountable size. We will survey applications from graph theory, the geometry of Euclidean spaces, topology, analysis and algebra. We will cover inductive constructions based on elementary submodels; coherent maps, walks on ordinals and applications of rho-functions; and various approximation schemes. We shall also point out several open problems that wait to be solved. The course aims to provide a working mathematician's toolbox without going too deep into any one specific area. The course is aimed at advanced bachelor and graduate students with an interest in combinatorial questions, set theory or logic.

  • Please find the course syllabus here.

  • Follow this link to the University's official course listing.

  • Assignments, course information and all related course materials will be posted on Moodle. In addition to the office hours, you will have the chance to ask questions and discuss the topics on the Moodle forum.

  • Lecture notes (no more updates).

  • Reading list (choose one for your final presentation).

  • Problem sets and last days you can submit solutions:


past teaching


University of Calgary:
img
2016 Winter: MAT265 University Calculus I.


University of Toronto:

2015 Summer: MAT135H1F with Yuri Cher, course website.

2014 Fall: MAT136H1F with Daniel Rowe, course website.

2014 Summer: MAT135H1F with Ivan Khatchatourian, course website.

2012-14: MAT1000/MAT1001 Analysis with Almut Burchard.


Eötvös Loránd University:

2010-11: Topics in General Topology,
exercise sheets: 1st 2nd 3rd 4th 5th 6th



Outreach



img

Public-key cryptography

  • My Hungarian and English presentations. This guides the first 45 minutes of discussion. We talk about the history of coding, modern requirements and various real-life scenarios. I bring an actual chain and locks to demonstrate the Diffie-Hellman key-exchange.

  • In the second part, class activities are based on Bell et al., Keller et al. and Rosemond.

  • We use graphs, as the public key, to code a natural number. First, the students work in pairs to code numbers for us. Then, they try to decode a number that was coded by us. While the students calculate, we decode their cyphers quickly by knowing an exact dominating set in the graph; the latter is the private key.

  • We discuss complexity, speed, how to generate keys and whether this particular technique is applicable in real life.



  • Past lectures: Eötvös József Gimnázium (2018/10/18), ELTE Trefort Ágoston Gyakorló Gimnázium (2018/11/12).




Further materials



Teaching dossier: download here (password protected).