Research Interests
- Extremal combinatorics
- Poset saturation
- Ramsey theory
- Ergodic theory
- Combinatorics on words
- Combinatorial games
- Additive combinatorics
Dr Maria-Romina Ivan is a pure mathematician with a primary focus on extremal combinatorics. Hailing from Romania, Dr Ivan embarked on her academic journey at the University of Cambridge in 2015, where she successfully completed her bachelor's, master's, and PhD degrees. From a young age, mathematics captivated her, and she eagerly participated in mathematical contests, fostering a deep-rooted passion for the subject. Over time, mathematics has transformed into more than a mere interest for Dr Ivan—it has become an integral part of her lifestyle, driving her dedication to exploring the depths of this fascinating field.
Dr Ivan hails from Pitești, a small city in Romania, where her love for mathematics was ignited at a tender age through participation in mathematical Olympiads. Over a span of nine years, she steadily advanced in these competitions, ultimately achieving international recognition with prestigious medals. Driven by her passion for mathematics, she secured a full scholarship to attend the esteemed International Computer High School of Bucharest (ICHB), where she completed her education in 2015.
In pursuit of her academic aspirations, Dr Ivan embarked on a journey to Cambridge in 2015 to study mathematics at St John's College. During her undergraduate years, she had the extraordinary opportunity to spend her second year at MIT as part of the Cambridge-MIT Exchange program. This experience proved to be transformative on both personal and academic levels, as she embraced a new culture while adapting to a different academic system.
Dr Ivan found great fulfilment in her third year having already covered substantial coursework at MIT, she was able to delve into a multitude of challenging subjects per term, allowing her time to engage in outreach initiatives and teach students at various events and camps.
Building upon her solid foundation, Dr Ivan proceeded to pursue Part III and successfully completed her BA and MMath degrees in June 2019, marking a significant milestone in her academic journey.
As a dedicated PhD student, Dr Ivan devoted her scholarly pursuits to extensive research. Throughout her doctoral journey, she explored various subjects, with poset saturation and Ramsey theory standing out as particularly noteworthy.
Dr Ivan's contributions to the field of poset saturation are evident through her two single-author papers, which significantly enhanced the lower bound on the poset saturation number for key posets, including the butterfly, poset N, and diamond. In her most recent paper, completed in collaboration with her summer research student Irina Ðanković, they not only determined exact values for the saturation number of small antichains but also proposed a conjecture that has recently been confirmed for general antichains.
In the realm of Ramsey theory, Dr Ivan achieved a remarkable milestone with her groundbreaking paper titled "A Ramsey Characterisation of Eventually Periodic Words." This pioneering work marked the first-ever connection between Ramsey theory and combinatorics on words. Dr Ivan presented this influential result at the prestigious international conference Ultramath 2022, held in Pisa, Italy.
In addition to her research endeavours, Dr Ivan actively engages in various academic activities, including the rewarding task of supervising undergraduate students. Drawing from her own experiences as a former student, she deeply appreciates the invaluable support she received from enthusiastic supervisors, which has left a lasting impact on her academic journey. Now, as a supervisor herself, she embraces the opportunity to offer guidance and assistance to her students.
Recognizing that mathematics can sometimes appear daunting, Dr Ivan takes on the role of a supportive supervisor, adept at unravelling the complexities and unveiling the inherent beauty of the subject. Her objective is to demystify mathematical concepts, enabling her students to perceive the elegance and wonders that she finds in mathematics. Guided by a genuine desire to help others, Dr Ivan strives to create an environment where learning is a pleasurable and enlightening experience for her students.
2019 - 2023: PhD in Pure Mathematics, St John's College, University of Cambridge
2018 - 2019: Master of Mathematics (MMath), St John's College, University of Cambridge
2015 - 2018: Bachelor of Arts, Mathematical Tripos, St John's College, University of Cambridge
2016 -2017: Massachusetts Institute of Technology (MIT), as part of the Cambridge-MIT Exchange Program.
2011 -2005: International Computer High School of Bucharest (ICHB), Bucharest, Romania
Saturation for the Butterfly Poset
Mathematika, 66 (2020), 806 – 817
Minimal Diamond-Saturated Families
Contemporary Mathematics, 3 (2022), 81 – 88
A Ramsey Characterisation of Eventually Periodic Words
Bulletin of the London Mathematical Society, 54 (2022), 2437 – 2455
Joint with I. Leader and L. Q. Zamboni
Constructible Graphs and Pursuit
Theoretical Computer Science, 930 (2022), 196 – 208
Joint with I. Leader and M. Walters
Saturation for Small Antichains
The Electronic Journal of Combinatorics, 30 (2023), #P1.3
Joint with I. Ðanković
Small sets in union-closed families
The Electronic Journal of Combinatorics, 30 (2023),#P1.8
Joint with D. Ellis and I. Leader
Some New Results on Monochromatic Sums and Products in the Rationals
New York Journal of Mathematics, 29 (2023), 301 – 322
Joint with N. Hindman and I. Leader