Participants

Ait El Manssour Rida ~ I am a first year PhD student at the MPI, my research interest is focused on differential algebra. My background is in differential geometry, random algebraic geometry, and p-adic numbers.

Alexandr Yulia ~ My mathematical interests are in combinatorics and algebraic geometry. I am a second year PhD student at Berkeley working with Bernd. I have taken the first algebraic geometry course at Berkeley this past semester. I have also seen a little bit of Grassmannians and Schubert calculus in Bernd’s class, but I don’t know too much about them.

Améndola Cerón Carlos ~ My main research interests lie in algebraic statistics. Enumerative geometry is playing an increasingly important role in understanding algebraic invariants in statistics such as the maximum likelihood degree. I am therefore excited to learn more about the principles of intersection theory.

Barban Lorenzo ~ I am Lorenzo Barban, a first year PhD-student at the University of Trento (where I did both my bachelor and my master degree) working under the supervision of prof. L.E. Solà Conde and prof. E. A. Romano. My main research interest is algebraic geometry, in particular the interplay between rational homogeneous varieties and birational geometry. I have attended some courses on riemann surfaces, toric geometry and birational geometry. I'm also interested in tensor geometry.

Belotti Mara ~ I am Mara Belotti and I am currently a first year Phd student in Berlin under the supervision of prof. Michael Joswig. For my master thesis I worked with algebraic topology. Right now I am focusing on a project about realization spaces of polytopes and I plan on studying toric geometry.

Bik Arthur ~ I am a postdoc at MPI Leipzig in the Nonlinear Algebra group. My interests lie in the intersection of Algebraic Geometry and Representation Theory, particularly the geometry of (structured) tensors of varying sizes. I have seen the words "Chow ring" multiple times and look forward to understanding what they mean.

Breiding Paul ~ For the Bachelor and the Master I studied Algebraic Number Theory. During my PhD I moved to other topics: sensitivity of numerical algorithms for tensor decompositions, and counting real eigenvalues of random tensors. After my PhD I started developing software for numerically solving systems of polynomial equations. I am interested in all aspects of numerical or probabilistic methods in algebraic geometry. This includes both theoretical work and implementing effective methods.

Brysiewicz Taylor ~ My research is in computational algebraic geometry which, put simply, is the study of solving polynomial equations using computers. Solving can be done either symbolically or numerically, and I have particular interest in proving theorems using combinations of these two types of tools. I am also interested in enumerative geometry since knowing the number of solutions to a polynomial system prior to computation is a necessary step in a numerical proof. My favorite objects are families of varieties whose degrees have interesting combinatorial structure.

Çelik Türkü Özlüm ~ I work algebraic geometry from the lens of computation with an eye on applications. Lately, my focus has gravitated towards algebraic curves and their connections to integrable systems. In particular, I study algebro-geometric methods for a differential equation, the so-called KP equation, applying current methods from nonlinear algebra.This research area is centred around theta functions and closely related to the Schottky problem.

Chen Xiangying ~ I am a PhD student at Otto-von-Guericke Universität Magdeburg. I'm interested in algebraic combinatorics, polyhedral, tropical and algebraic geometry, especially their applications on combinatorial structures such as matroids, gaussoids and Coxeter matroids. I always encountered intersection theory because it connects algebraic geometry and matroids, however I have no background on it and would like to learn more about it.

Clarke Oliver ~ I am a 3rd year PhD student at the University of Bristol. I am particularly interested in commutative algebra, algebraic geometry, tropical geometry and their applications. My research involves understanding families of complicated objects from these areas through the lens of combinatorics. For example, toric degenerations of Schubert varieties by matching fields.

Danelon Alessandro ~ I am Alessandro Danelon, a phd student at the end of the second year from the university of Technology in Eindhoven. My research interest lies in applied algebraic geometry, commutative algebra and representation theory. More specifically, my Ph.D. project regards equivariant algebraic geometry and twisted commutative algebras. During my Ph.D. I worked on polynomial functors, a tool from representation theory that encodes infinite dimensional varieties with an action of GL (the infinite linear group). Besides this, I like algebraic number theory. I worked on modular forms for my master thesis studying a p-adic analogue for the class number formula.

De Lazzari Claudia ~ I’m a PhD student at the University of Trento. My research area is algebraic geometry. I’m interested in its “application” in the fields of quantum physics and quantum information. In particular I’m studying Tensor Network varieties from a geometrical point of view. They are varieties of tensors whose structure is defined by a graph and they have a relevance in quantum physics since theymodel/approximate interesting states in quantum many-body problems. In the master thesis I studied some geometrical constructions inferred by topological invariants of compact Kahler manifolds. Now, I’m deepening my knowledge in tensor decomposition and representation theory.

Duff Tim ~ I am interested in basic methods of computational algebraic geometry and their various applications, such as computer vision. Developing tools for numerical algebraic geometry and studying polynomial systems with "structure" (eg. imprimitive Galois group) have been major threads in my research so far. I'm eager to learn more about intersection theory to get a better perspective on these topics.

Dye Stefan ~ I graduated from McMaster University in Canada with a degree in electrical engineering and have worked in industry primary writing software doing algorithmic computations for natural language understanding, or image processing. I have developed interests in algebraic geometry, combinatorics, my mathematical background was focused on solving differential equations, and applying optimization and control theory to engineering problems. I hope to use my learnings from this course to learn about intersection-theoretic tools, ground my understanding of algebraic geometry and to broaden my mathematical horizons.

El Maazouz Yassine

Fairchild Samantha ~ My background is studying Riemann surfaces from a dynamical point of view. Specifically I have spent most of my time studying geodesic flows on specific Riemann surfaces by analyzing subsets of the plane corresponding to closed geodesics. I am interested in building more algebraic tools to study the moduli spaces of Riemann surfaces as well as taking my dynamical knowledge to work on more algebraically defined spaces.

Fevola Claudia ~ My main research interests are Algebraic Geometry and related areas. In particular, my Master studies were focused on geometry and the classical geometry of curves and surfaces in projective space. At the moment I’m studying Riemann surfaces and Algebraic Curves and I’m interested in families of solutions arising from Riemann surfaces to the KP partial differential equation. Also by joining the LSSM project at the MPI in Leipzig some application of Algebraic Geometry to Algebraic Statistics (e.g. the study of the maximum likelihood degree) and Enumerative Geometry (e.g. counting the numbers of quadrics tangent to 9 given quadrics in real 3-space) appeared in my research.

Fife Tara ~ I received a PhD from Louisiana State University in 2020, working under James Oxley. My background is in combinatorics with an emphasis in structural matroid theory. Since graduate school, I have been broadening my mathematical knowledge so that I can work on the types of algebraic geometry that involves matroids.

Flavi Cosimo ~ My research interests are focused on some subjects of algebraic geometry, like multilinear algebra and tensor decomposition; in particular, my research activity is currently based on the determination of the symmetric tensor rank and the decompositions of specific symmetric tensors, considered as homogeneous polynomials.

Franceschini Alberto ~ My research area is algebraic geometry over the complex numbers. Specifically, I am interested in torus actions over projective (smooth) varieties X. I have studied such actions when X was a rational homogeneous variety G/P. Pasquier described some examples of quasi-homogeneous varieties (the so called horospherical varieties) and Occhetta, Romano, Sola Conde and Wisniewski prove that these varieties can be constructed using (bandwidth one) C*-actions on rational homogeneous varieties. So, with Lorenzo Barban, we are trying to generalize this construction to produce new examples of quasi-homogeneous varieties with a C*-action.

Galgano Vincenzo ~ My research interests are about Tensor Decomposition in Algebraic Geometry: in this area I have received some research proposals (both theoretical -envolving rational homogeneous varieties- and more applied -envolving entanglements in tensor networks and ground states) but I am still considering which one to choose. However I am also interested in other topics in Algebraic Geometry, even with links to Algebraic Number Theory, envolving algebraic groups, group cohomology and Representation Theory. My background includes homological algebra, infinite Galois Theory, ramification of primes in number fields, complex semisimple Lie algebras, fundamentals of Algebraic Topology, sheaf theory, vector bundles on complex manifolds.

Garrote-López Marina ~ I'm a PhD student at the Universitat Politècnica de Catalunya. I am particularly interested in applied algebraic geometry and algebraic statistics. My current research is focused on algebraic phylogenetics, more precisely in studying phylogenetic inference using algebraic and semi-algebraic tools. I've recently started studying intersection theory and I think this course will help me to gain a deeper understanding of the topic.

Homs Roser ~ I did my PhD in Commutative Algebra and I recently started working in Algebraic Statistics. I came across with intersection theory in a recent project. I would like to start from scratch and I think this course is a good oportunity.

Hosten Serkan ~ My background is in computational and combinatorial algebraic geometry, such as toric ideals/varieties and the polyhedral combinatorics that goes with it. My applied interests are in optimization (integer programming), algebraic statistics (hierarchical models, ML degree), and more recently in sum-of-squares (Gram spectrahedra).

Kühne Lukas ~ I am a former PhD student of Karim Adiprasito in Jerusalem. My research interests lie at the intersection of algebra and combinatorics. A main project of my phd research was concerned with generalized matroid representations such as over matrix rings or division rings. Moreover, I enjoy studying hyperplane arrangements algebraically (via their derivation module), combinatorially (via their intersection lattice), and how these concepts interplay with each other. Recently, I am looking into tropical geometry and its applications in neural networks and physics. I have taken some algebraic geometry classes during my studies but never studied intersection theory.

Kuppel Tim ~ I am a third year bachelor student of mathematics at the University of Konstanz. Mainly I am interested in Representation Theory and Algebraic Geometry; in particular I am looking forward to learning more about their relation.

Julia Lindberg ~ I am primarily interested in applied algebraic geometry, specifically applications arising in statistics, engineering and optimization. I have taken classwork in algebraic geometry, commutative algebra and topology but I know very little about enumerative geometry and intersection theory in general.

Melánová Hana ~ Since my bachelor's degree, I have been working on resolution of singular curves, itself a subfield of algebraic geometry. The goal of my PhD thesis was to use tools and techniques from different areas like algebraic and differential geometry, commutative algebra and invariant theory in order to resolve singularities in a geometric way. I will join Bernd's group at the Max Planck Institute in April. I am looking forward to learn about the principles of enumerative geometry and intersection theory which are both new to me.

Meroni Chiara ~ I am a first year PhD student at the MPI MiS in Leipzig , working in the Nonlinear Algebra Group. My background is mainly in topology, algebraic topology and real algebraic geometry. The goal of my PhD is to study convex geometry and try to create a bridge between the analytic and the algebraic geometric point of view.

Motwani Harshit J ~ I am mostly interested in Algebraic geometry, Combinatorial Commutative Algebra, Tropical Geometry and their applications to Algebraic Statistics. Currently, I am working on solving some questions related to a family of matroid varieties and also working on cellular resolutions for a special family of ideals. I have basic knowledge of Commutative Algebra covering most parts of Atiyah-Macdonald. I have taken a course on Algebraic Geometry covering Chapter 1 of Hartshorne. I am also familiar with scheme theory covering First 11 chapters of Ravi Vakil's notes.

Oghbaei Mehri ~ I am a Math PhD student at Sharif University of Technology in Iran, working on special polynomials like real stable and log-concave ones and their applications in counting and sampling and finding approximation algorithms. These concepts are related to geometry and algebra too, for example, chow ring, hodge theory and ... which I know only basic things.

Rodriguez Jose Israel ~ My background is in applied algebraic geometry and algebraic statistics. I enjoy develop methods for solving systems of polynomial equations, especially those involving Galois groups. My favorite applications of AG are to non-linear eigenvalue problems and maximum likelihood estimation.

Rydell Felix ~ Bachelor's and Master's at the University of Gothenburg in pure mathematics. I'm a PhD student at KTH in algebraic geometry and A.I with Kathlén Kohn and Fredrik Viklund as supervisors. My interests are algebraic geometry, polyhedral geometry, spectral geometry, complex analysis and number theory.

Santarsiero Pierpaola ~ I'm a 3rd year Ph.D. student of the University of Trento, Italy. My research focuses on the identifiability of tensors and tensor decomposition. So I work with secant varieties of Segre varieties. I'm familiar with basic concepts of algebraic geometry but I'm completely new to enumerative geometry.

Sendra Javier ~ My mathematical interest is focused on theoretical applied or computational Algebraic Geometry. My Master Thesis is about Gromov Witten Theory. However, my background on Intersection Theory is not very good and I feel this course could improve it a lot. About my mathematical background, I have taken courses about algebraic geometry (two courses), Moduli Spaces of Curves, Singular Homology and Cohomology, Commutative Algebra, Representation Theory, De Rham Cohomology and currently coursing a subject about Algebraic Stacks.

Seynnaeve Tim ~ I recently graduated at the MPI in Leipzig and am now a postdoc at the University of Bern. I'm interested in algebraic geometry, representation theory, and their connections to various applications. I recently encountered some enumerative geometry in a project where we studied maximum likelihood degrees in algebraic statistics via the space of complete quadrics. Another topic related to intersection theory that fascinates me is the connection between algebraic geometry and matroids.

Shehu Elima ~ I will be a PhD student in the Research Group "Numerical and Probabilistic Nonlinear Algebra”, my interests are on "sensitivity in computer vision". My background related to the course topic is: linear algebra and geometry, abstract algebra, real and functional analysis, introduction to topology.

Staffolani Reynaldo ~ I am a third year Ph.D. student at the University of Trento. My research is focused on tensor decomposition of tensors arising from SL(n)-rational homogeneous varieties. I am familiar with basic notions of algebraic geometry and I know a little of Representation Theory but I am completely new to enumerative geometry.

Telen Simon ~ I graduated from KU Leuven (Belgium) as a mathematical engineer and did my PhD on solving systems of polynomial equations. My main mathematical interests are in computational algebraic geometry, more specifically system solving (algebraic and homotopy techniques), toric/tropical geometry, tensors, ... I hope to use the material of the course to develop effective computational methods and to learn about intersection-theoretic tools for proving root counts.

Turatti Ettore ~ My research interest is on Algebraic Geometry, focusing on multilinear algebra, tensor decomposition and algorithms for the Waring decomposition of polynomials. Currently I have been looking to understand properties of the eigenscheme of a tensor, working on questions such as given an eigenscheme configuration, which are the tensors that have those eigentensors and how to recover them from this scheme.

Vater Paul ~ I am a PhD student at the MPI Leipzig and part of the mathematical software group, as well as a developer of the software system Polymake. This means i like implementing mathematical/algorithmic ideas in software, and on the other hand using software to aid my research. Roughly speaking I care about discrete geometry, and its connections to other areas of mathematics such as algebraic geometry or topology. In particular this includes tropical geometry and patchworking. At the moment i am thinking about real tropical lines.

Martin Vodička ~ I am a third year Phd student at the MPI in Leipzig. My research interest lies mostly in combinatorial structures in algebraic geometry, e.g. toric varieties and polytopes. I was also using some enumerative geometry when I was working on the project about ML-degrees and complete quadrics.

Vu Truong ~ I am interested in the interaction between combinatorics, algebraic geometry, and analysis.

Weigert Julian ~ I currently study math at the University of Konstanz and im in semester 5. My main interests at the moment are algebraic geometry and combinatorics although i am not very experienced in these topics since i only know them since this semester. Im also learning about basic matroid theory at the moment which i find very interesting too.

Winter Rosa ~ My background is in arithmetic geometry, which is the interplay between number theory and algebraic geometry. In my PhD I studied surfaces (specifically del Pezzo surfaces); I studied both their geometry as well as their rational points (the points where all coordinates are rational numbers). Since September I am a postdoc in the group of Bernd Sturmfels at the Max Planck Institute in Leipzig, where I want to learn more about ways to apply geometry (in algebraic statistics, for example). Enumerative geometry is new for me.