Zacharias Veiksaar, Bachelor's thesis, K33

Date and time: Thursday 28/8, 8:30
Place: Cramér meeting room, Albano building 1
Student: Zacharias Veiksaar
Supervisor: Yishao Zhou
Title: "A Study of Portfolio Optimization in Discrete Time: From Markowitz to Reinforcement Learning"

Abstract

This paper investigates portfolio optimization in discrete time, covering its development from the classical mean-variance framework, multi-period extensions, and modern reinforcement learning approaches. We begin with a rigorous treatment of the single-period case, deriving analytical solutions, highlighting their sensitivity to estimation errors, and proposing regularization as a solution to this sensitivity. We then extend the framework to a multi-period setting using dynamic programming, where we encounter time-inconsistency in the mean-variance formulation and propose a time-consistent reformulation that we solve analytically. As the reliance on estimating asset return distributions remains we propose reinforcement learning as a suitable model-free alternative, circumventing the need for explicit estimation of these parameters. We reformulate the time-consistent multi-period problem as a Markov decision process, prove that optimal solutions exist and argue these can be found within the reinforcement learning framework. The results highlight the mathematical structure of portfolio optimization, provide a broad treatment of limitations in classical approaches, and lay the groundwork for more robust machine learning methods as an alternative. 

Nikolina Bellon, Master's thesis, M5

Date and time: Thursday 28/8, 9:00
Place: Meeting room 25, Albano building 2
Student: Nikolina Bellon
Supervisor: Wushi Goldring
Title: "Semisimple Lie algebras and root systems"

Abstract

This thesis classifies finite-dimensional complex semisimple Lie algebras using their root systems. The first part defines Lie algebras, ideals, semisimplicity, solvability and representations. We establish their basic properties. The key is Cartan’s criterion for semisimplicity. The second part focuses on semisimple Lie algebras. We prove the existence of Cartan subalgebras and root space decomposition. This leads to studying root systems. We classify reduced and irreducible root systems via the correspondence between semisimple Lie algebras and their root systems. This yields the classification of semisimple Lie algebras.

Emre Kaplaner, Bachelor's thesis, K25

Date and time: Thursday 28/8, 10:00
Place: Cramér meeting room, Albano building 1
Student: Emre Kaplaner
Supervisor: Yishao Zhou
Title: "Dynamic Mean–Variance Portfolio Choice: Markowitz Foundations, Time Inconsistency, and Game-Theoretic Equilibria"

Abstract

This thesis investigates dynamic mean–variance portfolio optimization with a focus on the fundamental challenge of time inconsistency. In the classical single-period setting, one obtains a clear risk–return trade-off via a quadratic optimization, but extending to multiperiod or continuous-time horizons reveals that variance penalties cannot be nested in the usual recursive optimization framework. To overcome this, we adopt a game-theoretic intrapersonal approach in which each date-t decision-maker is treated as a “player” sharing the same preferences but controlling only that period’s choice. A time-consistent policy is then defined as a subgame-perfect equilibrium: no future self can profitably deviate when all others stick to the prescribed strategy. We derive the corresponding extended Bellman recursions in discrete time and outline the continuous-time analogue as an equilibrium HJB system. By solving these equations in representative examples, we demonstrate a tractable method for generating dynamically credible mean–variance strategies that respect real-world constraints.

Johannes Erixon, Bachelor's thesis, K24

Date and time: Thursday 28/8, 10:30
Place: Meeting room 41, Albano building 2
Student: Johannes Erixon
Supervisor: Wushi Goldring
Title: "Jordan Normal Form"

Abstract

This thesis explores Jordan Normal Form as a method for analyzing linear operators, especially when diagonalization fails. Through examples and theory, it demonstrates how functions such as e^A, sin(A) and log(I+A) can be computed using the Jordan structure, revealing deeper algebraic properties of operators.

Anton Christenson, Master's thesis, M6

Date and time: Thursday 28/8, 10:30
Place: Meeting room 25, Albano building 2
Student: Anton Christenson
Supervisor: Peter LeFanu Lumsdaine
Title: "Functorial Semantics for Fragments of First-Order Logic"

Abstract

Functorial semantics provides a close connection between logic and category theory, where models of a theory can be seen as functors out of a classifying category. This perspective also shows how set-theoretic models can be generalized in a natural way to models in any other category with the appropriate structure.
    
In this thesis we introduce functorial semantics first for algebraic theories and then for intuitionistic first-order logic, and show how the categorical framework can be used to prove soundness and completeness of the corresponding deductive systems.

Different treatments of this topic make different equivalent choices both on the logical side (in terms of which deductive rules to include) and on the categorical side (in terms of which extra structure to require). We aim here to make the connection between the two sides as clear as possible, by stating the structural requirements in a way that directly mirrors the deductive rules. This approach also simplifies the process of comparing and contrasting different logical fragments, such as regular and coherent logic.

Lucas Dixon Leijon, Bachelor's thesis, K26

Date and time: Thursday 28/8, 12:30
Place: Meeting room 41, Albano building 2
Student: Lucas Dixon Leijon
Supervisor: Rikard Bögvad
Title: "Hyperbolic Groups"

Abstract

In this paper we will define and describe hyperbolic groups and some relevant mathematical concepts such as hyperbolic metric spaces, Cayley graphs and quasi-isometries. As well as giving some proofs for the equivalence of a few different definitions of hyperbolic metric space and stating and proving the Švarc–Milnor lemma.

Olli Pettersson, Independent projects for mathematics teachers, L14

Date and time: Thursday 28/8, 13:00
Place: Meeting room 9, Albano building 1
Student: Olli Pettersson
Supervisor: Per Alexandersson
Title: "The Geometry of a Good Cut: Moser, Pizza, and Beyond"

Abstract

How many regions can be formed by connecting points on a circle with straight lines? What appears at first to be a simple geometric exercise quickly unfolds into a rich interplay between combinatorics, geometry, and topology. This thesis explores a family of classic problems involving partitions of space—starting with Moser’s circle problem, extending through inductive reasoning, binomial identities, Euler’s characteristic, and considerations of higher-dimensional analogues. Along the way, we uncover the seductive illusion of exponential patterns, harness the structure of Pascal’s triangle, and reflect on how different mathematical perspectives—combinatorial, visual, and topological—can complement one another. A variety of approaches are explored to shed light on the creative and multifaceted nature of mathematics—qualities that often stand in contrast to how the subject is presented in traditional curricula, where time and space for multiple methods are rare. This work aims to celebrate mathematical thinking as an art of variation and discovery.

Rubina Parvin, Bachelor's thesis, K30

Date and time: Thursday 28/8, 14:00
Place: Meeting room 25, Albano building 2
Student: Rubina Parvin
Supervisor: Sofia Tirabassi
Title: "Generating functions and their applications to counting"

Abstract

This thesis investigates generating functions and their applications in combinatorial enumeration, emphasizing how these tools simplify the process of counting complex, structured objects. It provides a clear introduction to ordinary, exponential, and Dirichlet generating functions, explaining their definitions, uses, and connections to problems in combinatorics, analysis, and number theory.

The thesis examines how algebraic operations on exponential generating functions correspond to fundamental combinatorial constructions, such as combining, partitioning, and relabeling labeled sets. It also demonstrates how generating functions can be used to solve recurrence relations, using the Catalan numbers as a key example.

A major focus is the Exponential Formula, which relates the generating functions of connected components to the generating function of the total structure they form. Through the framework of cards, decks, and hands, this result is illustrated with applications to permutations and labeled graphs. Overall, the thesis presents generating functions as powerful and unifying tools in modern combinatorics.

More presentations in August

You can find upcoming presentations in the calendar

The following projects will also be presented in August.

Sindre Becker, Bachelor's thesis, K22
Date and time: Tuesday 19/8, 9:00
Place: Meeting room 25, Albano building 2
Student: Sindre Becker
Supervisor: Jakob Reiffenstein
Title: "Primtals satsen genom Newmans Tauberiska sats för Laplace transformationen och Riemanns zetafunktion"

Ottilia Andersson, Bachelor's thesis, K21
Date and time: Wednesday 27/8, 9:00
Place: Cramér meeting room, Albano building 1
Student: Ottilia Andersson
Supervisor: Wushi Goldring
Title: "Outer automorphisms of S6"

Axel Olsson, Bachelor's thesis, K28
Date and time: Wednesday 27/8, 9:00
Place: Meeting room 25, Albano building 2
Student: Axel Olsson
Supervisor: Yishao Zhou
Title: "Convergence Analysis of Quasi Newton methods and on the relation to Conjugate Gradient"

David Sermoneta, Bachelor's thesis, K31
Date and time: Wednesday 27/8, 10:30
Place: Meeting room 25, Albano building 2
Student: David Sermoneta
Supervisor: Salvador Rodriguez-Lopez
Title: "A guided tour of Wavelet theory via the constructions of Multiresolution analyses"

Ludvig Fagrell, Master's thesis, M7
Date and time: Wednesday 27/8, 12:30
Place: Meeting room 25, Albano building 2
Student: Ludvig Fagrell
Supervisor: Annemarie Luger
Title: "Rational Herglotz-Nevanlinna functions of several variables"

Filip Ström, Bachelor's thesis, K32
Date and time: Wednesday 27/8, 14:00
Place: Meeting room 41, Albano building 2
Student: Filip Ström
Supervisor: Samuel Lundqvist
Title: "En experimentell studie av termreduktion med Gröbnerbaser och en alternativ algoritm"

Anya Hanson, Master's thesis, M8
Date and time: Wednesday 27/8, 14:00
Place: Meeting room 25, Albano building 2
Student: Anya Hanson
Supervisor: Salvador Rodriguez Lopez
Title: "Solvability of Dirichlet and Neumann Boundary Value Problems on C^{1,α} Domains"

Yue Su, Independent projects for mathematics teachers, L15
Date and time: Friday 29/8, 9:00
Place: Cramér meeting room, Albano building 1
Student: Yue Su
Supervisor: Per Alexandersson
Title: "Avgörbara och oavgörbara problem-en analys utifrån strategiska spel"

Titti Westlin, Bachelor's thesis, K34
Date and time: Friday 29/8, 10:30
Place: Cramér meeting room, Albano building 1
Student: Titti Westlin
Supervisor: Per Alexandersson
Title: "Bevis av Lindström-Gessel-Viennots lemma samt några tillämpningar."

Erika Berger, Bachelor's thesis, K23
Date and time: Friday 29/8, 11:00
Place: Meeting room 25, Albano building 2
Student: Erika Berger
Supervisor: Wushi Goldring
Title: "From Abstraction to Action: Exploring Symmetry through Group and Representation Theory"

Minna Litzén, Bachelor's thesis, K27
Date and time: Friday 29/8, 13:00
Place: Cramér meeting room, Albano building 1
Student: Minna Litzén
Supervisor: Håkan Granath
Title: "Fibonacci modulo m"

Dennis Partanen, Bachelor's thesis, K29
Date and time: Friday 29/8, 13:00
Place: Meeting room 25, Albano building 2
Student: Dennis Partanen
Supervisor: Pavel Kurasov
Title: "Solving the Schrödinger equation by example"

Jorge Martín, Master's thesis, M9
Date and time: Friday 29/8, 13:30
Place: Zoom
Student: Jorge Martín
Supervisor: Alexander Berglund
Title: "The Halperin conjecture"

Marcus Ibrahim, Independent projects for mathematics teachers, L13
Date and time: Friday 29/8, 14:30
Place: Cramér meeting room, Albano building 1
Student: Marcus Ibrahim
Supervisor: Håkan Granath
Title: "Permutationsgrupper"