* Seuraavan viikon tapahtumat merkitty tähdellä
Prof. Andrea Pinamonti (Università di Trento)
A Gentle Introduction to Sub-Riemannian Geometry
* Wednesday 04 February 2026, 10:15, M3 (M234)
In this talk, we introduce the main ideas of sub-Riemannian geometry, and briefly describe some of its applications and open problems.
Seminar on analysis and geometry / Korte
Professor Anders Christian Hansen, University of Cambridge, UK
Necessary mechanisms for super AI and stopping hallucinations: The consistent reasoning paradox and the indeterminacy function.
Tuesday 10 February 2026, 15:15, M1 (M232)
Creating Artificial Super Intelligence (ASI) (AI that surpasses human intelligence) is the ultimate challenge in AI research. This is, as we will discuss, fundamentally linked to the problem of avoiding hallucinations (wrong, yet plausible answers) in AI. We will describe a key mechanism that must be present in any ASI. This mechanism is not present in any modern chatbot and we will discuss how, without it, ASI will never be achievable. Moreover, we reveal that AI missing this mechanism will always hallucinate. Specifically, this mechanism is the computation of what we call an indeterminacy function. An indeterminacy function determines when an AI is correct and when it will not be able to answer with 100% confidence. The root to these findings is the Consistent Reasoning Paradox (CRP), which is a new paradox in logical reasoning that we will describe in the talk. The CRP shows that the above mechanism must be present as surprisingly an ASI that is pretty sure (more than 50%) can rewrite itself to become 100% certain. It will compute an indeterminacy function and either be correct with 100% confidence, or it will not be more than 50% sure. The CRP addresses a long-standing issue that stems from Turings famous statement that infallible AI cannot be intelligent, where he questions how much intelligence may be displayed if an AI makes no pretence at infallibility. The CRP answers this consistent reasoning requires fallibility and thus marks a necessary fundamental shift in AI design if ASI is to ever be achieved and hallucinations to be stopped.
Department Colloquim
Anestis Tzogias (U. Neuchatel)
The Arakelov class group and hard cryptographic problems on ideal lattices
Thursday 12 February 2026, 16:00, M237
Euclidean lattices are a trendy topic from the applied side, as they are a very promising candidate for constructing quantum-resistant cryptographic protocols, based on hard problems such as the Shortest Vector Problem (SVP). Ideal lattices are a class of lattices coming from ideals in number fields, and recently they have been getting attention for allowing efficient implementation of cryptographic lattice protocols, with perhaps the most famous being based on the Learning With Errors problem. From the mathematical side, the space of all ideal lattices up to isometry is an object well-known to number theorists, called the Arakelov class group. We will discuss a result of de Boer et al. which uses random walks on the topological structure of the Arakelov class group and the Extended Riemann Hypothesis to relate the average-case and worst-case instances of the SVP problem on ideal lattices.
ANTA Seminar / Hollanti et al.
Dr. Lucas Hataishi (University of Oxford)
TBA
Tuesday 17 February 2026, 10:15, M3 (M234)
Romain Usciati (Paris-Saclay)
TBA
Tuesday 24 February 2026, 10:15, M3 (M234)
Milla Laurikkala
Midterm review
Tuesday 24 February 2026, 11:15, M2 (M233)
Lorenzo Zacchini (Aalto University)
Fractional integrals on spaces of homogeneous type
Wednesday 25 February 2026, 10:15, M3 (M234)
Analysis seminar / Hytönen
Theo Elenius
Midterm review
Wednesday 04 March 2026, 10:15, M3 (M234)
n this talk, we discuss higher integrability for Cauchy-Dirichlet problems for systems of parabolic $p$-Laplace type in noncylindrical domains $E \subset \mathbb{R}^n \times \mathbb{R}$.
Under suitable assumptions on $E$, the gradient of a weak solution is integrable up to the lateral and initial boundaries beyond the natural exponent $p$.
The talk is based on joint work with Kristian Moring and Christoph Scheven.
Seminar on analysis and geometry
Dr. John Urschel (MIT)
TBA
Tuesday 10 March 2026, 15:15, U5 (U147)
Riku Anttila (University of Jyväskylä)
TBA
Wednesday 11 March 2026, 10:15, M3 (M234)
Seminar on analysis and geometry
Sylvester Eriksson-Bique (University of Jyväskylä)
TBA
Wednesday 11 March 2026, 11:15, M3 (M234)
Seminar on analysis and geometry
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Thursday 12 March 2026, 09:00, TBA
Further information
Ohjelma: https://mycourses.aalto.fi/course/view.php?id=34597#module-908887
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 08 May 2026, 09:00, TBA
Further information
Ohjelma: https://mycourses.aalto.fi/course/view.php?id=34597#module-908887
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Monday 15 June 2026, 09:00, TBA
Further information
Ohjelma: https://mycourses.aalto.fi/course/view.php?id=34597#module-908887
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