I am a postdoctoral researcher in the Browning Group at the Institute for science and Technology Austria. Before I was a Ph.D. candidate at Leiden University under the supervision of dr. Martin Bright. My research is on arithmetic geometry as I apply geometric techniques to study questions in number theory. I am for example interested in local to global principles such as the Hasse principle and several forms of approximation to both rational and integral points, obstructions to these principles (the Brauer-Manin obstruction, to name one), the counting of points of bounded height, but also effective techniques for points on curves and surfaces. I am fascinated by the endless geometric techniques one can use to study some obvious and seemingly simple questions in number theory. |
Contact: Julian Lyczak jlyczak (at) ist.ac.at IST Austria Am Campus 1 A – 3400 Klosterneuburg |

- Log K3 surfaces with a Brauer-Manin obstruction of order 5 to the Hasse principle. (To appear soon)
- Arithmetic of affine del Pezzo surfaces, Ph.D. thesis, Leiden University, 2019.
- A uniform bound on the Brauer groups of certain log K3 surfaces, joint with Martin Bright. Published in Michigan Mathematical Journal, volume 68(2), 2019, pp. 377–384.

- Arithmetic of affine del Pezzo surfaces

Ph.D. thesis, written under the supervision of Martin Bright - Cobordism theories: An algebraic journey from topology to geometry

Master thesis, written under the supervision of Carel Faber - Knowledgeable Frobenius algebras and extended topological quantum field theories

Bachelor thesis, written under the supervision of Ieke Moerdijk

- Notes on spectral sequences.

- Monodromy of the generalized hypergeometric equation in the Frobenius basis, by Leslie Molag. Published in Indagationes Mathematicae in 2015, pages 495-518.
- On the equation \(x+y=1\) in finitely generated groups in positive characteristic, by Peter Koymans and Carlo Pagano.

- "Bonte was"

Article on a problem from the Baltic Way 2015, Pythagoras, February 2016 - "Nines, nines, more nines"

is a translation of the article "Negens, negens en nog meer negens". This article was published in the book

"Half a Century of Pythagoras Magazine"

MAA Press, 2015.

This book and its articles are a translation of the "De Pythagoras Code" into English. - "De veelzijdigheid van de zeshoek"

Article on a problem from the Dutch National Mathematical Olympiad 2013, Pythagoras, June 2013

jointly with Daniël Kroes - "Op en neer met de roltrap"

Article on a problem from the Dutch National Mathematical Olympiad 2011, Pythagoras, February 2011 - "Een extreem handig principe"

Article on the Extremal Principle, Pythagoras, April 2013 - "Ramsey-kardinalen"

Article on Ramsey cardinals, Vakidioot, Number 2, 2011-2012 - "De Monstergroep"

Article on the monster group, Vakidioot, Number 4, 2010-2011 - "De Grieken tegen de Japanners"

Article on angle trisection by paper folding, Vakidioot, Number 1, 2010-2011 - "Projectieve meetkunde"

Article on projective geometry, Vakidioot, Number 3, 2009-2010

jointly with Sjoerd Boersma - "IMO 2006 - Opgave 4"

Article on a problem from the International Mathematical Olympiad 2006, Euclides, October 2010 - "Negens, negens en nog meer negens"

Article on a problem from the Dutch National Mathematical Olympiad 2009, Pythagoras, February 2009

This article was also selected, among all articles published by Pythagoras in the last 50 years, for publication in the book

"De Pythagoras Code"

Uitgeverij Bert Bakker, Amsterdam, 2011 - "Materiaal voor de finaletraining van de Nederlandse Wiskunde Olympiade"

Material to prepare high school students for mathematical competitions, 2008

jointly with dr. Birgit van Dalen and dr. Quintijn Puite

- Magma code to compute the subgroups of the finite automorphism group of the Picard group of del Pezzo surfaces.
- Magma code to compare the first cohomology groups of subgroups of the Weyl group acting on two free \(\mathbb Z\)-modules. This is used to compare the algebraic Brauer group of a log K3 surface with an irreducible ample anticanonical bundle, to the Brauer group of the corresponding del Pezzo surface.

- Why do I want to learn about Coleman–Chabauty? At An informal seminar on the method of Chabauty and Coleman, IST.
- Manin's conjecture for lattices

At the Browning group working seminar at IST.

- On the study of integral points in families

At the Browning group working seminar at IST.

- The geometry of integral points

At the Browning group working seminar at IST. - Explicit examples of Brauer–Manin obstructions to integral points

At the Browning group working seminar at IST.

- Brauer-Manin obstructions of order 5 on log K3 surfaces

At the conference Rational Points on Schiermonnikoog. - What it is I do

At the PhD Colloquium in Leiden. - Abstract tropical curves

At the Tropical Geometry Seminar in Leiden.

- Explicit Brauer-Manin obstructions of order 5

At the DIAMANT symposium in Breukelen, The Netherlands. - Why your piano is never in tune!

A lunch lecture organized by De Leidsche Flesch in Leiden.

- A uniform bound on Brauer groups of certain log K3 surfaces

At XXX-émes Journées Arithmétic in Caen, France. - A uniform bound on Brauer groups of certain log K3 surfaces

In the Algebra, Geometry and Number Theory seminar. - Het Hasse-principe (in Dutch)

In the bachelor seminar algebra, geometry and number theory. - Obstructions to local-global principles on del Pezzo surfaces

In the seminar on Obstructions to local-global principles. - Spectral sequences

In the seminar on Obstructions to local-global principles. - Introduction to the etale fundamental group

in the seminar on Good reduction of abelian varieties at the University of Amsterdam.

- Trace fields of knots

in the Knot theory seminar at Leiden University.

- Nodal curves on surfaces, an application of algebraic cobordism

Presentation of master thesis in the Algebra, Geometry and Number Theory seminar

- Nodal curves on surfaces, an application of algebraic cobordism

Defense of master thesis

The slides were accompanied by a black board presentation - Taylor's formula

in a seminar on Vertex Operator Algebras - Obstruction theory

in a seminar on Characteristic Classes - Relative \(K_0\) and \(K_1\)

in a seminar on Algebraic K-theory

- Memorial conference for Sir Peter Swinnerton-Dyer, Newton Institute, Cambridge, May 5–7th, 2020. (unconfirmed)
- Arithmetic statistics and local-global principles, ESI, Vienna, July 20–24th, 2020
- Number theory program, Institut Mittag-Leffler, Sweden, January 11th– April 30th, 2021. (unconfirmed)

- An informal seminar on the method of Chabauty and Coleman, IST. (co-organizer)

- Topics in Rational and Integral Points, Basel, Switzerland, September 2th–13th, 2019.

- À la Redécouverte des Points Rationnels, Institut Henri Poincaré, Paris, June, 2019.
- Rational points on Fano and similar varieties, Institut Henri Poincaré, France, May 20th–24th, 2019.
- Geometric and Analytic Methods for Rational Points, CIRM, France, April 14th–19th, 2019.
- Winter School: Trace functions and their applications, Monte Verità, Switzerland, January 13th–18th, 2019.

- Algebra, Geometry and Number Theory seminar, Leiden.
- Intecity seminar, The Netherlands.
- General colloquium, Leiden.
- PhD colloquium, Leiden.

- Algebraic Statistics, Leiden, Autumn 2018.
- DIAMANT symposium, Veenendaal, November 29–30th, 2018.
- 14th Belgian-Dutch Algebraic Geometry Day, Nijmegen, September 20th–21st, 2018.

- 14th Belgian-Dutch Algebraic Geometry Day, Nijmegen, September 20th–21st, 2018.

- Rational Points on Schiermonnikoog, Schiermonnikoog, July 2nd–6th, 2018.
- DIAMANT symposium, Veldhoven, April 4th–5th, 2018.
- Nederlands Mathematisch Congres, Veldhoven, April 3rd–4th, 2018.
- Tropical Geometry Seminar, Leiden, spring 2017.

- Néron model seminar, Leiden, autumn 2017.
- 12th Belgian-Dutch Algebraic Geometry Day, Nijmegen, December 15, 2017.
- DIAMANT symposium, Breukelen, November 30th–December 1st, 2017.
- Topics in arithmetic and algebraic geometry, Mainz, Germany, October 9th–13th, 2017.
- Diophantine Problems (DIOP), Manchester, England, September 11th–15th, 2017.
- IRTG Summer school, Texel, August 27th–September 1st, 2017.

- XXX-émes Journées Arithmétic, Caen, France, July 3rd–7th, 2017.
- DIAMANT symposium, Breukelen, June 1st–2nd, 2017.
- Nederlands Mathematisch Congres, Utrecht, April 11th–12th, 2017.
- Obstructions to local-global principles, Leiden, spring 2017. (co-organizer)
- Logarithmic geometry seminar, Leiden, spring 2017.
- Kloosterman seminar, Leiden, autumn 2016 & spring 2017.
- Good reduction of abelian varieties, UvA, autumn 2016 & spring 2017.
- Mini-workshop on K3-surfaces, Amsterdam, January 31, 2017.

- Good reduction of abelian varieties, UvA, autumn 2016 & spring 2017.
- Kloosterman seminar, Leiden, autumn 2016 & spring 2017.
- 11th Belgian-Dutch Algebraic Geometry Day, Amsterdam, December 9, 2016.
- DIAMANT symposium, Soest, November 25th–26th, 2016.
- Crystalline cohomology, UvA, autumn 2016.
- IRTG Summer school, Vlieland, August 28th–September 2nd, 2016.

- Crash course on Shimura varieties, Leiden, June 20–22nd, 2016.
- DIAMANT symposium, Veenendaal, May 26–27th, 2016.
- Ramification theory seminar, Leiden, spring 2016.
- Rational points on elliptic curves, Leiden, spring 2016.
- Etale cohomology seminar, Leiden, autumn 2015 & spring 2016.
- 10th Belgian-Dutch Algebraic Geometry Day, Leuven, April 22, 2016.
- BeNeLux Mathematical Congress, Amsterdam, March 22nd–23rd, 2016.
- Knot theory seminar, Leiden, spring 2016. (co-organizer)

- DIAMANT symposium, Lunteren, November 26–27th, 2015.
- Etale cohomology seminar, Leiden, autumn 2015 & spring 2016.
- Moduli stacks seminar, Leiden, autumn 2015.

- Algebraic Geometry Seminar: B-NL meets NoGAGS, Nijmegen, June 11–12th, 2015.
- DIAMANT symposium, Veenendaal, May 28–29th, 2015.
- Seminar on Local Galois representations, Leiden, spring 2015.
- Nederlands Mathematisch Congres, Leiden, April 14–15th, 2015.
- Arizona Winter School, Tucson, March 14–18th, 2015.
- Seminar on K3 surfaces and their automorphisms, Leiden, autumn 2014 and spring 2015.

- Galois Groups and Fundamental Groups
- Vertex Operator Algebra
- Characteristic Classes
- Algebraic K-theory seminar

- Lineaire algebra 1 voor natuurkundigen (in Dutch)

- Mathematical reasoning at the Leiden University College.
- Wiskundewedstrijdtraining (in Dutch)

- Lineaire algebra 1 (in Dutch)
- Wiskundige structuren (in Dutch)
- Wiskundewedstrijdtraining (in Dutch)

- Algebra 1 (in Dutch)
- Wiskundewedstrijdtraining (in Dutch)

- Wiskundewedstrijdtraining (in Dutch)
- Elliptic curves (MasterMath)

- Wiskundewedstrijdtraining (in Dutch)

- Mathletico, the soccer team of the Mathematical Institute
- Applied game theory seminar (co-organizer)
- The MI BBQ, September 2018 (co-organizer)