What exactly is number theory, and what drives researchers to dedicate their careers to this field? How does this seemingly abstract branch of mathematics connect to the cryptography that secures our digital world?

A couple of weeks ago, Luxembourg hosted the 33rd Journées Arithmétiques, providing us with the perfect opportunity to explore these questions. We sat down with two mathematicians: a visiting researcher and a local expert, offering insights from both international and Luxembourg-based perspectives.

Our first guest is Prof. Jennifer Balakrishnan from Boston University, who led the team that cracked the notorious "cursed curve" problem. We couldn't resist discussing it and learning more from Jennifer about current big questions.

We also explored the mathematical foundations of cryptography with Tim Seuré, a PhD student at the Faculty of Science, Technology and Medicine (FSTM) at the University of Luxembourg, focusing on fully homomorphic encryption.

USEFUL LINKS:

More about Prof. Jennifer Balakrishnan: https://math.bu.edu/people/jbala/

Quanta Magazine article about cracking the "cursed curve": https://www.quantamagazine.org/mathematicians-crack-the-cursed-curve-20171207/

33rd Journées Arithmétiques: https://www.uni.lu/fstm-en/conferences/ja25/

Great Internet Mersenne Prime Search: https://www.mersenne.org/

In this episode, Professor Elisabeth Letellier from the University of Luxembourg and Dr. Mina Tsenkova, now at Amgen in California, discuss colorectal cancer research and ketogenic diet. Mina won the Rolf Tarrach Award 2024 for her PhD thesis.

The discussion centers around the critical role of the gut microbiome in cancer development, specifically how diet influences this relationship. Mina shares insights from her award-winning PhD research on the ketogenic diet and its effects on colorectal cancer, while Elisabeth provides an overview of the disease itself and the rising incidence among younger populations. Together, they explore the complexities of diet, microbiome interactions, and the challenges of translating research into clinical practice.

USEFUL LINKS

Rolf Tarrach Award for Dr. Mina Tsenkova - https://www.uni.lu/research-en/events/rolf-tarrach-award-2024/

Amgen - https://www.amgen.com/

Science in Colours - Mina Tsenkova - https://www.youtube.com/watch?v=OGhgWsezc7c

Dr. Patrick Michel, senior researcher at CNRS and global fellow at the University of Tokyo, discusses how our understanding of asteroids has evolved dramatically since the mid-1990s. Early research relied on reflected light observations, but space missions have revealed asteroids as complex geological worlds with diverse shapes and structures. Patrick reflects on this transition from limited knowledge to groundbreaking missions that reveal the intricate features of these celestial bodies.

The episode also covers Asteroid Day, celebrated annually on June 30th, which commemorates the 1908 Tunguska event when an asteroid explosion destroyed a large area of Siberian forest.

Moreover, Patrick recounts the successful DART mission, which tested asteroid deflection techniques and demonstrated humanity's first deliberate alteration of a celestial body's trajectory. He introduces also the Hera mission, designed to investigate the aftermath of the DART impact on asteroid Dimorphos, gathering crucial data on asteroid composition and structure.

USEFUL LINKS

Hera mission - https://www.heramission.space/

More about Dr. Patrick Michel - https://www.oca.eu/michel/

DART mission - https://science.nasa.gov/mission/dart/

NASA’s OSIRIS-REx - https://science.nasa.gov/mission/osiris-rex/

Asteroid Foundation - https://asteroidfoundation.org/