The students talks displayed in this page are ordered by alphabetical order of the speakers, with respect to their first names. The schedule can be consulted on the schedule page.
The talks will take place at the main building in the room H0107 of TU Berlin. More information on the venue and how to find the talks can be found on the venue page.
Many talks were recorded on video, but the video is released publicly only upon permission of the speakers; you can find all the videos using this link.
Our conference is going to feature talks from two invited speakers and fifteen student speakers:
A "holomorphic curve" is a complex analytic mapping from a compact Riemann surface to a complex projective variety. These objects and their generalizations play an important role in algebraic geometry and symplectic topology. The space of holomorphic curves (of a fixed topological type) is a priori non-compact, but a fundamental theorem due to Gromov shows that any sequence escaping to infinity in this space has a subsequence converging to a "holomorphic curve with mild singularities". After explaining this result, I'll focus on its converse: given a singular holomorphic curve, when is it actually realizable as the limit of a sequence as above? I'll present a partial answer to this, which turns out to be intimately connected to the classical theory of meromorphic functions on compact Riemann surfaces (based on joint work with Fatemeh Rezaee).
The video of the talk can be accessed in this link.
More information about Mohan Swaminathan can be found here.
Why does a Spaghetti usually break into more than just two pieces? We investigate this observation by means of a mathematical model for dynamic crack propagation. For this, we introduce a phase-field method as well as generalized derivatives in terms of subdifferentials. We provide a mathematical model given as a coupled system of non-smooth partial differential equations and discuss suitable notions of weak solutions. We prove their existence using a fully discrete approximation of the problem and study their behavior in numerical simulations.
More information about Marita Thomas can be found here.
Biological membranes are thin structures that are composed of various components. The different components often form microdomains, called lipid rafts, that are arranged in complex patterns. To explain this pattern formation, variational models based on Cahn-Hilliard type energies have been introduced that couple the local composition of the membrane to its local curvature, which renders the resulting functionals nonlocal.
The main focus of this talk lies on the derivation of the \( \mathcal \Gamma\)-limit in a certain parameter regime where the limiting functional turns out to be of perimeter-type. As a main novelty, we will present a technique to include Neumann-boundary conditions in the construction of a recovery sequence. Additionally, in the remaining parameter regimes scaling behavior of the infimal energy will be discussed.
The video of the talk can be accessed in this link.
Given a polytope in \( \mathcal n\)-dimensional space, how can we deform it "infinitesimally" such that the resulting shape is still convex? This question appears naturally when we look for extremal bodies of certain geometric functionals. In my talk, I will discuss an abstract notion of small (i.e., infinitesimal) perturbations of convex bodies. It turns out that these small perturbations can be represented by signed measures on the boundary of the convex body. I will discuss a full characterization of the set of realizable signed measures in the case that the perturbed body is a polytope.
The video of the talk can be accessed in this link.The Fast Multipole Method is a widespread method to speed up \( \mathcal N\)-body calculations and enable simulations on large scales. In the project for my Master thesis, I developed a machine learning algorithm, more specifically a graph neural network, which uses the same hierarchical structure as the FMM and has the same benefits of speeding up the computation. I also tested this hierarchical GNN on problems from computational chemistry, i.e. prediction of properties of molecules from their molecular graph.
The video of the talk can be accessed in this link.
We discuss the basics of realizable matroids, and closely associated objects called realization spaces. We use software to study large datasets of matroid realization spaces, and produce examples of reducible and singular spaces.
The video of the talk can be accessed in this link.
Scheduling jobs with given processing times on identical parallel machines so as to minimize the sum of their completion times is one of the most basic scheduling problems. We study interesting generalizations of this classical problem involving a finite number of scenarios. In our model, a scenario is defined as a subset of a predefined and fully specified set of jobs. The aim is to find an assignment of the whole set of jobs to identical parallel machines such that the schedule, obtained for the given scenarios by simply skipping the jobs not in the scenario, optimizes the average sum of completion times over all scenarios.
We conjecture a structural property of optimal schedules, which implies a polynomial-time algorithm for this problem, and prove special cases of this conjecture using diverse methods in combinatorics and polyhedra.
The geometry of compactifications of the moduli space of abelian varieties can be leveraged to deduce modularity theorems of formal Siegel-Jacobi forms.
Are you wondering what the recent excitement about Lean is about? What the formalisation of deep theorems (such as the liquid tensor experiment, sphere eversion or the unit fractions project) means? Why we would be interested in doing this? I will answer all these questions and give an impression of the current state of things. There will also be some pointers to how to get involved.
This talk centers on low-dimensional manifolds, i.e.,3 and 4 dimensions, approaching them from both a topological viewpoint and through the rich lenses of contact and symplectic geometry. We explore the common tools employed for understanding them and highlight the increased complexity introduced by contact and symplectic structures.
The video of the talk can be accessed in this link.
I would like to talk about a problem of partitioning a convex polygon in \( \mathcal R^2\) into \( \mathcal R^n\) convex pieces of equal area and equal perimeter. The natural extension of this problem in \( \mathcal R^d\) has been proven only when the number of pieces \( \mathcal n \) is a prime power. I will explain how this problem translates to a question in Algebraic Topology, touch on what is known and what are the obstacles. The talk is based on a recent paper of mine with Pavle Blagojević.
The video of the talk can be accessed in this link.
In this talk, we delve into the world of mathematical modelling as a tool for understanding and predicting the spread of infectious diseases. Navigating through the complexities of epidemiology, we explore how mathematical models serve as virtual laboratories, allowing us to simulate and analyse different scenarios. Key to this are stochastic sampling algorithms. We discuss strategies to accelerate stochastic simulations while maintaining robust accuracy
This work proposes a method for learning the long-term dynamics of slowly changing battery aging parameters (capacity and internal resistance) starting from fast changing measurements. The methodology combines the use of Kalman Filters at the fast time scale to estimate the slow-scale parameters and Artificial Neural Networks on the slow time scale to learn a model for the slowly changing battery aging parameters.
The video of the talk can be accessed in this link.
Green growth proposes the reduction of greenhouse gas emissions while the economy grows and there is prosperity for all. However, how to induce a transition from our current economic model to a carbon-neutral economy is still undetermined. The Green Growth mechanics model is a strongly simplified Ramsey model for two times steps. It incorporates technical progress through learning-by-doing, directed technical progress for brown and green capital stock, and a labor market with search. This model provides insights for the discussion about the possibilities of green growth. In this talk I would take you through the agentization of the endogenous technical progress building block of the Green Growth mechanics along the lines of agent-based modelling. We consider utility maximizing agents that adopt different investment strategies based on the information available to them. Also I would present you results from this agentization process.
The Ehrhart quasipolynomial of a rational polytope P encodes fundamental arithmetic data of P, namely, the number of integer lattice points in positive integral dilates of P. Ehrhart quasipolynomials were introduced in the 1960s, satisfy several fundamental structural results and have applications in many areas of mathematics and beyond. I will give an introduction to Ehrhart Theory, explaining the objects involved, fundamental results, and some research questions. The enumerative theory of lattice points in rational (equivalently, real) dilates of rational polytopes is much younger, starting with work by Linke (2011), Baldoni-Berline-Koeppe-Vergne (2013), and Stapledon (2017). We introduce a generating-function ansatz for rational Ehrhart quasipolynomials, which unifies several known results in classical and rational Ehrhart theory. In particular, we define y-rational Gorenstein polytopes, which extend the classical notion to the rational setting. This is joint work with Matthias Beck and Sophia Elia.
Most of us in the symplectic topology group in Berlin work on the theory of pseudo-holomorphic curves and its applications to symplectic/contact topology. In this talk, I will start by defining a Pseudo-holomorphic curve. Then, I will explain its few applications in symplectic geometry.
Embark on a 30-minute journey through the fascinating realm of Riemannian geometry, delving into the intricate structures of special holonomy spaces such as Calabi-Yau manifolds, G2 manifolds, and Spin(7) manifolds. This talk will unravel the connections between these geometric objects and their pivotal role in the theoretical framework of Super String theory and M theory. Discover the construction methods employed in the creation of Spin(7) manifolds and the significance of Spin(7)-Instantons, showcasing the rich interplay between geometry and physics. The exploration extends to Cayley submanifolds, shedding light on their role in shaping our understanding of higher-dimensional spaces. Join us for a concise yet comprehensive exploration of these captivating topics at the crossroads of mathematics and theoretical physics.