eva-maria hainzl

Hi!

I am mathematician, currently working as a post-doc at LIX, École Polytechnique
in France. Before I worked at DMG, TU Wien, where I received my PhD in 2024.

My research is concerned with discrete structures that decompose
recursively (such as branching structures). My goal is to find and describe
universal properties for the large scale behavior thereof. I primarily employ
techniques from analytic combinatorics but I also have a strong affinity
for probabilistic methods and like problems with geometric flavor.

Contact me!

Research

Discrete differential equations

Discrete differential equations appear in the enumeration of lattice paths, polyominoes, planar maps, intervals of the Tamari lattice, fighting fish, parking trees and many more. They were also the central object of study in my PhD thesis.

Singularly perturbed discrete differential equations (with Michael Drmota)
Asymptotic normality of pattern occurrences in random planar maps II
Asymptotic normality of pattern occurrences in random planar maps (with Michael Drmota and Nick Wormald)
Universal asymptotic behavior of positive functional equations with catalytic variable (with Michael Drmota)

PhD thesis: Singularity analysis of discrete differential equations and applications

Tree walks

Tree walks are closed walks on a complete graph, constrained to span trees. Several subclasses thereof appear in the computation of moments of the spectral measure of various random matrix models, for example in the spectral distribution of random graphs.

Formulas and asymptotics of hypergraph catalan numbers
Tree walks and the spectrum of random graphs (with Élie de Panafieu)

Others

Here is some other unrelated things that I did for fun (e.g. for my master’s thesis):

Geometric dominating sets (with Oswin Aichholzer and David Eppstein)
Finding a battleship of uncertain shape (with Maarten Löffler, Daniel Perz, Josef Tkadlec and Markus Wallinger)

Master’s thesis: Geometric dominating sets

Teaching

Université Paris-Saclay, Orsay, FR

2026 Analytic Combinatoris (Lecture, M2, joint with Élie de Panafieu)

TU Wien, Vienna, AT

2023 Analysis 2 for Computer Science students (Exercise Classes, Bachelor)
2021/22 Discrete and Geometric Algorithms for Math students (Exercise Classes, Master)
2020/21 Discrete and Geometric Algorithms for Math students (Exercise Classes, Master)
2020/21 Discrete Mathematics for Computer Science students (Exercise Classes, Master)

Technical University of Leoben, Leoben, AT

2020 Analysis for Engineering students (Exercise Classes)
2020 Mathematics of Economics for Engineering students (Exercise Classes)

Karl-Franzens University of Graz, Graz, AT

2019 Analysis 1 for Math students (Tutorials, Bachelor)

University of Technology Graz, Graz, AT

2017/18 Probability Theory and Stochastic Processes for Computer Science students (Exercise Classes, Bachelor)
2017/18 Statistics for Computer Science students (Exercise Classes, Bachelor)
2017/18 Statistics for Math students (Exercise Classes, Bachelor)
2017/18 Probability Theory and Stochastic Processes for Electrical Engineering students (Exercise Classes, Bachelor)

Scientific activities

Talks

4. February 2026 Asymptotic normality of pattern counts in random planar maps, JCB, Bordeaux, FR
4. November 2025 Introduction to functional equations with catalytic variable, AG DM, Vienna, AT
26. September 2025 Tree walks and the spectrum of random graphs, RandNet Workshop, Vienna, AT
3. September 2025 Submap counts in random planar maps, The Annual 2025 ÖMG-DMV Meeting, Linz, AT
5. August 2025 Pattern occurrences in random planar maps, RS&A, Vienna, AT
29. September 2023 [Poster] Hunting bears in random planar maps, ICERM Workshop, Providence, US
2. August 2023 Hunting bears in random planar maps, SCAAEC 2023, Bedlewo, PL
14. July 2023 Characteristic singularities of universality classes, SIAM AG23, Eindhoven, NL
18. April 2023 Exhaustive tree walks and the spectrum of random graphs, AG DM, Vienna, AT
14. April 2023 A glimpse of the spectrum of graphs by walking on trees, VSM student retreat, Ysper, AT
9. February 2023 Universal types of singularities of solutions to equation systems, NTAG Seminar, SFU, CA
24. January 2023 Universal coefficient asymptotics of solutions to catalytic equations, AG DM, Vienna, AT
27. October 2022 Pattern occurrences in planar maps, Seminar combinatoire numérative et analytique, IRIF, FR
21. June 2022 Universal properties of catalytic variable equations, AofA2022, Philadelphia, USA
3. June 2022 Geometric dominating sets – Revenge of the pawns, Student Symposium in Combinatorics, AU
12. May 2022 Generating functions and universal laws on coefficient asymptotics, PhD colloquium, AT
22. April 2022 Hitting, packing, covering problems and further surprises, VSM student retreat, Ysper, AT
21. March 2022 Singularity analysis for catalytic equations, Journées Aléa, CIRM, FR
2. February 2022 Counting with generating functions, 2nd Austrian day of women in mathematics, AT
20. November 2021 Universal asymptotics of catalytic variable equations, SFB Status Seminar, AT
29. September 2021 Geometric dominating sets on the discrete torus, Graduate Online Combinatorics Colloquium
4. April 2021 Geometric Dominating Sets – A Minimum Version of the No-3-In-Line Problem, EuroCG’21, RU
17. November 2020 Geometric Dominating Sets, AG Diskrete Mathematik (AG DM), Vienna, AT

Conferences, workshops and research visits

9.-13. March 2026 Journées Aléa, Luminy, FR
12.-16. January 2026 Workshop in Enumerative Combinatorics, Oberwolfach, DE
8.-12. September 2025 SFB Summer School, Pörtschach am Wörthersee, AT
16.-19. June 2025 GAPCOMB Workshop, Poblet, ES
4.-10. May 2025 AofA2025, Toronto, CA
16.-21. March 2025 Journées Aléa, Luminy, FR
7.-12. January 2024 Workshop Community in Algebraic and Enumerative Combinatorics, Banff, CA
26.-30. July 2023 AofA2023, Taipeh, TW
13.-17. March 2023 Journées Aléa, Luminy, FR
22.-30. August 2022 RandNet Workshop on Random Graphs, Eindhoven, NL
1.-5. August 2022 Random Structures & Algorithms 2021/2022, Gniezno, PL
19.-25. September 2021 VSM Summer School, Weissensee, AT
28. June – 2. July 2021 Austrian Computational Geometry Reunion Meeting, Strobl, AT
21.-25 June 2021 Lattice Path Conference, CIRM, Luminy, FR

Other

I used to work as a graphic designer in nice places like Mürzzuschlag, Graz, Paris and Mauritius. So every once in a while I help out family, friends and colleagues (e.g. Slides of ERC project POCOCOP).

I also have a degree in Stage and Costume Design, obtained at the University for Music and Performing Arts in Graz in 2015 and worked a bit in theatre but the only one that I dress up occasionally anymore is my dog Brezel..

Last update: April 2026