#### About me

I am a Taussky-Todd Instructor at Caltech, working with Alexander S. Kechris. I am interested in descriptive set theory and its connections to different fields, such as combinatorics, measure and group theory.

E-mail: vidnyanz_at_caltech_edu

Office: Linde 308

#### Publications

24. J. Frisch, A.S. Kechris, F. Shinko, ZV: Realizations of countable Borel equivalence relations, work in progress.

23. A. Medini, ZV: Zero-dimensional \sigma-homogeneous spaces, submitted.

22. S. Brandt, Y. Chang, J. Grebik, C. Grunau, V. Rozhon, ZV: Local Problems on Trees from the Perspectives of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics, submitted.

21. J. Grebik, ZV: Tall F_\sigma subideals of tall analytic ideals,

*Proceedings of the American Mathematical Society, to appear.*

20. M. Elekes, M. Poor, ZV: Haar-positive closed subsets of Haar-positive analytic sets,
draft.

19. R. Carroy, B. D. Miller, ZV: On the existence of small antichains for definable quasi-orders,

*Journal of Mathematical Logic, to appear.*

18. R. Carroy, B. D. Miller, D. Schrittesser, ZV: A basis under injective homomorphism for definable graphs with chromatic number at least three, *in preparation*. A short summary of the results.

17. R. Carroy, B. D. Miller, D. Schrittesser, ZV: Minimal definable graphs of definable chromatic number at least three,

*Forum of Mathathematics Sigma, 9 (2021) e7.*

16. B. D. Miller, ZV: On the existence of large antichains for definable quasi-orders,

*Journal of Symbolic Logic 85 (2020), no. 1, 103-108.*

15. M. Elekes, D. Nagy, M. Poor, ZV: A Haar meager set that is not strongly Haar meager,

*Israel Journal of Mathematics 235 (2020), 91–109.*

14. R. Carroy, Y. Pequignot, ZV: Embeddability on functions: order and chaos,*Transactions of the American Mathematical Society 371
(2019) 6711–6738.*

13. S. Todorcevic, ZV: A complexity problem for Borel graphs,

*Inventiones Mathematicae (2021),* to appear.

12. P. Komjath, I. Leader, P. A. Russell, S. Shelah, D. T. Soukup, ZV: Infinite monochromatic sumsets for colourings of the reals,

*Proceedings of the American Mathematical Society 147
(2019) 2673–2684.*

11. U. Darji, K. Kalina, V. Kiss, M. Elekes, ZV: The structure of random automorphisms of the rational numbers,

*Fundamenta Mathematicae 250 (2020), 1–20.*

10. U. Darji, K. Kalina, V. Kiss, M. Elekes, ZV: The structure of random automorphisms of the random graph, *submitted.*

9. U. Darji, K. Kalina, V. Kiss, M. Elekes, ZV: The structure of random homeomorphisms,

*Israel Journal of Mathematics 237 (2020), 75–113.*

8. U. Darji, K. Kalina, V. Kiss, M. Elekes, ZV: The structure of random automorphisms of countable structures,

*Transactions of the American Mathematical Society 371
(2019) 8829–8848.*

7. B. Farkas, Y. Khomskii, ZV: Almost disjoint refinements and mixing reals,

*Fundamenta Mathematicae 242 (2018), 25-48.*

6. M. Elekes, ZV: Characterization of order types of pointwise linearly ordered families of Baire class 1 functions,

*Advances in Mathematics 307 (2017), 559–597. *

5. M. Elekes, ZV: Naively Haar null sets in Polish groups,

*Journal of Mathematical Analysis and its Applications 446 (2017), 193–200. *

4. M. Elekes, V. Kiss, ZV: Ranks on the Baire class \xi functions,

*Transactions of the American Mathematical Society 368 (2016), no. 11, 8111–8143.*

3. V. Kiss, ZV: Unions of regular polygons with large perimeter-to-area ratio,

*Discrete and Computational Geometry 53 (2015), no. 4, 878–889.*

2. M. Elekes, ZV: Haar null sets without G_\delta hulls,

*Israel Journal of Mathematics 209 (2015), no. 1, 199–214.*

1. ZV: Transfinite inductions producing coanalytic sets,

*Fundamenta Mathematicae 224 (2014), 155–174.*

PhD Thesis