Departamento de Ciências Matemáticas FCUL

01/06/2026

Seminário de Matemática Discreta
Title: Borders, Debordering, and Algebraic Complexity,
Speaker: Pranjal Dutta (Assistant Professor, CCDS, NTU, Singapore)

Abstract: The talk introduces Valiant’s framework for algebraic complexity—VP vs. VNP (determinant vs. permanent)—and its border variants. Border complexity underlies the best-known bounds on matrix multiplication. The talk focuses on two toy models defined by Waring and Chow ranks, surveys recent debordering results, compares structural behaviours of border and non-border measures, and outlines open problems. A longer survey can be found at arxiv.org/abs/2510.13049 (Invited and accepted in Text and Monographs in Symbolic Computation (TMSC) 2026).
*No prior knowledge of algebraic complexity, or advanced mathematics is required*.

Bio: Pranjal Dutta is currently an Assistant Professor in the College of Computing and Data Science (CCDS) at Nanyang Technological University (NTU) Singapore. He spent Fall 2025 at Simons Institute as a Simons-Berkeley Fellow as well as Jane Street Research Fellow. Before joining NTU, he was a postdoc at NUS Singapore, advised by Prof. Divesh Aggarwal. He obtained his PhD from Chennai Mathematical Institute, advised by Prof. Nitin Saxena and he was supported by Google PhD Fellowship. His PhD work won the ACM India Doctoral Dissertation Award 2023. He is broadly interested in Theoretical Computer Science, with a focus on algebraic complexity theory, and geometric complexity theory (GCT), learning theory, and related areas of mathematics.

28/05/2026

SEMINÁRIO DE LÓGICA MATEMÁTICA (SLM)
2025/2026 - year ###VII
CEMS.UL
Next week, we will have a talk by Paulo Guilherme Santos.

SLM :: SESSION #23 :: Monday, June 1, 15:00 (Lisbon time)
Paulo Guilherme Santos (IPMA Lisboa and CEMS.UL)

TITLE :: Reflexivity of Omega-Consistency in a General Setting

ABSTRACT :: How much can a mathematical theory certify about its own reliability? This question sits at the heart of metamathematics, and it grows especially delicate once we ask a theory to vouch for the consistency of its own fragments. A theory is called reflexive when it can prove the consistency of each of its finitely axiomatized sub-theories, and essentially reflexive when this ability survives the addition of any finite batch of new axioms. Peano Arithmetic, together with the standard set theories, enjoys this remarkable property.
In this talk we move beyond ordinary consistency to a richer family of reliability statements modelled on omega-consistency — the property that a theory never proves a claim for every individual natural number while simultaneously proving that some number fails it. We show that essentially reflexive theories are reflexive not only for ordinary consistency but also for its restriction to formulas of bounded quantifier complexity. Partial truth predicates take centre stage along the way, and they yield a strikingly short proof that a natural theory of truth built over Peano Arithmetic already establishes the full omega-consistency of arithmetic.

LOCATION :: Faculdade de Ciências da Universidade de Lisboa, Room 6.2.33

25/05/2026

25/05/2026

𝗖𝗼𝗻𝗵𝗲𝗰𝗲 𝗮𝘀 𝗹𝗶𝗰𝗲𝗻𝗰𝗶𝗮𝘁𝘂𝗿𝗮𝘀 𝗱𝗼 𝗗𝗲𝗽𝗮𝗿𝘁𝗮𝗺𝗲𝗻𝘁𝗼 𝗱𝗲 𝗖𝗶ê𝗻𝗰𝗶𝗮𝘀 𝗠𝗮𝘁𝗲𝗺á𝘁𝗶𝗰𝗮𝘀
📣Novas Datas📣
Alunos das Licenciaturas em Estatística Aplicada, Matemática e Matemática Aplicada de Ciências ULisboa convidam alunos do Ensino Secundário interessados em saber mais sobre estes cursos para uma conversa ONLINE.🛜
👉Licenciatura em 𝗠𝗮𝘁𝗲𝗺á𝘁𝗶𝗰𝗮 𝗔𝗽𝗹𝗶𝗰𝗮𝗱𝗮: dias 2 de junho às 18h e 19 de junho às 11h
👉Licenciatura em 𝗠𝗮𝘁𝗲𝗺á𝘁𝗶𝗰𝗮: dias 8 de junho e 7 de julho às 18h
👉Licenciatura em 𝗘𝘀𝘁𝗮𝘁í𝘀𝘁𝗶𝗰𝗮 𝗔𝗽𝗹𝗶𝗰𝗮𝗱𝗮: dias 9 de junho e 9 de julho às 18h
✍🏼Inscrição gratuita, mas obrigatória através do link: ( https://forms.gle/RWcSxT89xfkNasRYA ).
Os inscritos receberão informação mais detalhada sobre a sessão uns dias antes da mesma, por email. 📩

23/05/2026

DCM no "Feitos de Futuro", durante a tarde de 23 de maio.🌟

23/05/2026

📢Feitos de Futuro - Hoje, 23 de maio, estamos no Pavilhão de Portugal! 🌟Vem experimentar as atividades do DCM-FCUL! Vem divertir-te!✨ Esperamos por ti!

22/05/2026

SEMINÁRIO DE LÓGICA MATEMÁTICA (SLM)
2025/2026 - year ###VII
CEMS.UL

Next week, we will have a talk by Victor Barroso-Nascimento.
Please note that we will be returning to our usual schedule.
SLM :: SESSION #22 :: Monday, May 25, 15:00 (Lisbon time)

Victor Barroso-Nascimento (University College London)
TITLE :: Higher-order Kripke models for intuitionistic and other non-classical modal logics
ABSTRACT :: In this talk I will present higher-order ("nested") Kripke models, a generalization of Kripke models that is remarkably close to Kripke's original idea -- both mathematically and conceptually. Intuitionistic modal logics are used for the case study, as the generalisation is arrived at specifically after the paradigmatic cases of intuitionistic modal logics IK and MK are studied. Standard models are now 0-ary models, whereas n-ary models for n > 0 are models whose set of objects (''possible worlds'') contain only (n-1)-ary models. A key idea is the use of worlds as fixed points for modal definitions, in the sense that what is necessary or possible in a world of a frame depends only on what is true in the same world on the accessible frames. The association between conditions on accessibility relations and modal axioms also carries over to this framework, so modal logics stronger than K can be obtained by imposing requirements on the relations between frames. Just like Kripke models define a concept of ''alternative'' for classical models, the n-ary models (for n > 0) defines the same concept for any interpretation of the (n-1)-ary models. In particular, if we use the common interpretation of intuitionistic Kripke models as representing the activities of a mathematician in a particular timeline, modalities are defined in a natural way through the concept of alternative timelines.

15/05/2026

O DCM necessita de voluntários para a banca no dia 23 de maio (sábado) no evento “Experimenta o Futuro”, no Pavilhão de Portugal.

Temos três turnos:

Turno 1 – 10:00 às 13:00
Turno 2 – 13:00 às 15:00
Turno 3 – 15:00 às 18:00

Os interessados deverão enviar email para 𝗻𝘂𝗰𝗹𝗲𝗼𝗰𝟲@𝗰𝗶𝗲𝗻𝗰𝗶𝗮𝘀.𝘂𝗹𝗶𝘀𝗯𝗼𝗮.𝗽𝘁 até dia 𝟭𝟵 𝗱𝗲 𝗺𝗮𝗶𝗼 com 𝗻𝗼𝗺𝗲, 𝗻.º 𝗱𝗲 𝗲𝘀𝘁𝘂𝗱𝗮𝗻𝘁𝗲, 𝗻.º 𝗱𝗲 𝘁𝗲𝗹𝗲𝗺ó𝘃𝗲𝗹 𝗲 𝘁𝘂𝗿𝗻𝗼 𝗽𝗿𝗲𝘁𝗲𝗻𝗱𝗶𝗱𝗼.

As vagas são limitadas.

14/05/2026

Candidaturas abertas para os EVM 2026 até 30 de Maio. Não deixes para o último dia!