The Mathematical Multiverse

I shall speak about some recent developments on the subject of modal model theory for the Junior Logic Seminar at the University of Oxford. The talk, titled The Mathematical Multiverse, will take place at the Mathematical Institute on November 16, 2021 at 5PM UK time. Please contact Brian Tyrrell should you like to join us. […]

British Logic Colloquium PhD day

I gave a short introductory talk on modal model theory for the British Logic Colloquium PhD day, taking place at 1st September 2021 as a part of the BLC Annual Meeting 2021 at Durham University. I explained the general idea and gave an update on the progress of my research, pointing out some new directions towards which […]

Guardian: symbolic validation of orderliness in SGX enclaves

This time, on a different note. This is a joint work with Pedro Antonino, Senior Research Scientist at the Blockhouse Technology Limited, and A. W. Roscoe, Professor of Computing Science at Oxford University, Senior Research Fellow in Computer Science at University College Oxford, Director of the University College Oxford Blockchain Research Centre, and Founder and […]

Modal graph theory as a foundation of mathematics

This will be a talk for the Barcelona Set Theory Seminar, 17 March 2021 4 PM CET (3 PM UK, 4 PM Poland). I understand the talk will be held on Zoom; please contact Claudio Ternullo for access. Abstract. One can consider the class of all graphs as a Kripke model of possible worlds, where […]

Playing with pebbles on the multiverse

Please find a recording below of a mini-talk I gave during Set Theory in The United Kingdom @ Home on December 4, 2020. We generalize Ehrenfeucht–Fraïssé games from classic model theory to modal model theory with actuality. Please note that it has come to my attention during the talk that Sam Adam-Day had considered modal […]

Modal model theory

This blog post from August 2019 now includes an update with regard to a result that is now revoked. Research has its ups and downs… I would like to share with you a brief description of what I have been doing at Oxford for the past eight months. Since my adviser has already written about […]

A half-pie ratio

Allow me to tell you about an interesting construction I learned from the Stewart’s Calculus book. Start with a square of area one. Next, extend your current rectangle, alternately, on top or beside, by another rectangle of area one. The first 500 steps of this construction are shown below. If you watch the animation carefully, you […]

Think you have a choice? Vitali’s revenge

I learned a fascinating fact a few weeks ago at the Philosophy of Mathematics, graduate lecture seminar at the University of Oxford. That week’s discussion was led by Professor Hamkins and concerned a remarkable book Defending the Axioms: On the Philosophical Foundations of Set Theory written by Penelope Maddy, logic and philosophy of science Distinguished […]

What complex numbers can tell us about the Multiverse?

There is an ongoing debate among mathematicians and philosophers on the nature of the realm where all mathematical activities are performed. But, before I pose the problem, we need to answer a pertinent question: “A realm? Do you mean like… our minds or what?” No. I mean metaphysical entity mathematicians are studying just like physicists […]

Liar’s Paradox

This was a talk for “Academic English: Spoken Communication 2” that I gave last Thursday. Please note that this presentation was aimed for non-mathematicians and non-philosophers. Thus, I concealed any anxiety about the topic for clarity’s sake. There is a short clip on the second slide and a GIF on the third one. Unfortunately, these […]