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Former Research Group

Algebraic Geometry

A water wave from a plane quartic curve.

We do research in algebraic geometry, with a strong focus on interactions with other areas such as probability, statistics, mathematical physics and their applications. We are particularly interested in studying classical geometrical objects with new symbolic and numerical methods.

One of our long term projects is to develop a program to study and connect the various aspects - geometric, computational, tropical and applied - of Riemann's theta function. This is a fundamental object at a crossroad of many fields: most intriguingly it connects algebraic curves with the physics of water waves.

Source for the picture: The Dubrovin threefold of an algebraic curve" (arXiv:2005.08244, D. Agostini, T.O. Celik and B. Sturmfels)

Research Group Leader
01.10.20 31.12.22

Daniele Agostini

Eberhard Karls Universität Tübingen
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Publications

inJournal
2023
Daniele Agostini et al.

KP solitons from tropical limits

In: Journal of symbolic computation

BibTex

 DOI: 10.1016/j.jsc.2022.04.009 ArXiv: 2101.10392 Code: mathrepo.mis.mpg.de
inJournal
2023
Daniele Agostini et al.

On the irrationality of moduli spaces of K3 surfaces

In: Transactions of the American Mathematical Society

BibTex

 DOI: 10.1090/tran/8830 ArXiv: 2011.11025
inBook
2022
Daniele Agostini et al.

Numerical reconstruction of curves from their Jacobians

In: Arithmetic, geometry, cryptography, and coding theory 2021 : 18th international conference ; May 31-June 4, 2021 Centre International de Rencontres Mathématiques, Marseille, France

BibTex

 DOI: 10.1090/conm/779 ArXiv: 2103.03138
Preprint
2022
Paul Breiding et al.

The algebraic degree of coupled oscillators

BibTex

 ArXiv: 2208.08179
Preprint
2022
Yassine El Maazouz et al.

Sampling from \(p\)-adic manifolds

BibTex

 ArXiv: 2207.05911 Code: mathrepo.mis.mpg.de
inJournal
2022
Claudia Fevola et al.

The mathematical research-data repository MathRepo

In: Computeralgebra-Rundbrief

BibTex

 ArXiv: 2202.04022 Link: fachgruppe-computeralgebra.de
inJournal
2022
Enis Kaya

Explicit Vologodsky integration for hyperelliptic curves

In: Mathematics of computation

BibTex

 DOI: 10.1090/mcom/3720 ArXiv: 2008.03774
inJournal
2022
Askol Khovanskii et al.

Cohomology rings of quasitoric bundles

In: Filomat

BibTex

 DOI: 10.2298/FIL2219513K ArXiv: 2112.14970
inJournal
2022
Ivan Limonchenko et al.

Generalized virtual polytopes and quasitoric manifolds

In: Trudy Matematiceskogo Instituta Imeni V. A. Steklova

BibTex

 DOI: 10.4213/tm4272 ArXiv: 2204.00114
inJournal
2022
Ivan Limonchenko et al.

Generalized virtual polytopes and quasitoric manifolds [Translation from Tr. Mat. Inst. Steklova 318, 139-165 (2022)]

In: Proceedings of the Steklov Institute of Mathematics

BibTex

 DOI: 10.1134/S0081543822040095 ArXiv: 2204.00114
Preprint
2022
Ruben Merlijn van Dijk et al.

Computation of admissible Arakelov-Green functions on metrized graphs

BibTex

 ArXiv: 2208.05857
inJournal
2021
Daniele Agostini et al.

Computing theta functions with Julia

In: Journal of software for algebra and geometry

BibTex

 DOI: 10.2140/jsag.2021.11.41 ArXiv: 1906.06507
Preprint
2021
Daniele Agostini et al.

On algebraic theta divisors and rational solutions of the KP equation

BibTex

 ArXiv: 2112.03147
inJournal
2021
Daniele Agostini et al.

On the Schottky problem for genus-five Jacobians with a vanishing theta null

In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze

BibTex

 DOI: 10.2422/2036-2145.201909_013 ArXiv: 1905.09366
inJournal
2021
Daniele Agostini et al.

Pencils on surfaces with normal crossings and the Kodaira dimension of \(\overline{\mathcal{M}}_{g,n}\)

In: Forum of mathematics / Sigma

BibTex

 DOI: 10.1017/fms.2021.28 ArXiv: 2008.12826 Code: www.math.hu-berlin.de
inJournal
2021
Daniele Agostini et al.

The Dubrovin threefold of an algebraic curve

In: Nonlinearity

BibTex

 DOI: 10.1088/1361-6544/abf08c ArXiv: 2005.08244
inJournal
2021
Daniele Agostini et al.

Theta surfaces

In: Vietnam journal of mathematics

BibTex

 DOI: 10.1007/s10013-020-00443-x ArXiv: 2001.11385 Link: math.berkeley.edu
inJournal
2021
Taylor Brysiewicz et al.

Tangent quadrics in real 3-space

In: Le Matematiche

BibTex

 DOI: 10.4418/2021.76.2.4 ArXiv: 2010.10879 Code: mathrepo.mis.mpg.de
Preprint
2021
Eduard Duryev et al.

Eigenforms of hyperelliptic curves with many automorphisms

BibTex

 ArXiv: 2104.08920
inJournal
2021
Claudia Fevola et al.

Pencils of quadrics : old and new

In: Le Matematiche

BibTex

 DOI: 10.4418/2021.76.2.2 ArXiv: 2009.04334
All Group Publications
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