Department of Mathematics

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Shusterman jointly publishes proof of twin primes problem


Two mathematicians, Will Sawin of Columbia University and Mark Shusterman of University of Wisconsin-Madison, recently posted a proof of a version of one of the most famous open problems in mathematics. The result opens a new front in the study of the twin primes conjecture, which has bedeviled mathematicians for more than a century and has implications for some of the deepest features of arithmetic.

The twin primes conjecture concerns pairs of prime numbers with a difference of 2. The numbers 5 and 7 are twin primes. So are 17 and 19. The conjecture predicts that there are infinitely many such pairs among the counting numbers, or integers. Mathematicians made a burst of progress on the problem in the last decade, but they remain far from solving it.

The new proof solves the twin primes conjecture in a smaller but still salient mathematical world. They prove the conjecture is true in the setting of finite number systems, in which you might only have a handful of numbers to work with.

Read More:  https://www.quantamagazine.org/big-question-about-primes-proved-in-small-number-systems-20190926/

Jordan Ellenberg Elected A.D. White Professor at Large at Cornell


Jordan Ellenberg joins a Nobel Prize-winning physicist, another bestselling author and a leader in global sustainable agriculture are among six newly elected Andrew Dickson White Professors-at-Large at Cornell.

The professors-at-large program at Cornell sponsors up to 20 outstanding scholars and public intellectuals at one time, in the life sciences, physical sciences, humanities, social sciences and the arts.

In each three-year period during their term, professors-at-large visit campus for about a week while classes are in session, to interact with students and faculty and enliven the intellectual and cultural life of the university. The program sponsors up to six visits per academic year, and activities such as public lectures and seminars.

Their six-year terms are effective July 1, 2019 through June 30, 2025. Candidates are nominated by Cornell faculty members; appointments are considered following review and recommendation by a faculty selection committee.

Link:   http://news.cornell.edu/stories/2019/09/six-ad-white-professors-large-elected

Jordan Ellenberg's Hawking Index predicts book unreadability


In The Guardian, Jordan Ellenberg explains his own way of calculating a book’s unreadability, which he dubbed the Hawking Index. Ellenberg looked at the sections that readers have highlighted on Amazon’s Kindle e-readers, and infers that after they’ve stopped highlighting, they’ve probably stopped reading. Link: https://www.independent.co.uk/arts-entertainment/books/features/books-to-read-unread-tsundoku-hawking-index-malcolm-cowley-antilibrary-a8521901.html

Math alumnus named University of Denver Chancellor


The University of Denver has chosen Jeremy Haefner as its 19th chancellor. 

Haefner, who earned a master’s degree and PhD in mathematics from the University of Wisconsin-Madison in 1983 and 1986, respectively, joined the University of Denver in 2018, serving as provost and executive vice chancellor. He previously held the positions of provost and senior vice president for academic affairs at Rochester Institute of Technology for 10 years. 

As a mathematician, Haefner studied integral representation and module theory, and his research has been published in Communications in Algebra, the Journal of Algebra and American Mathematical Society, among other journals. He has also written on topics in higher education, such as supporting diversity in leadership and enhancing the student experience.  

Denise O’Leary, chair of the University of Denver Board of Trustees, stated that Haefner has done remarkable work in the past year, including championing transparency and respect for shared governance, spearheaded efforts to share more regular and thorough updates on budget processes and improved lines of communication. 

“Our community has, in Jeremy, a national thought leader in student and academic success, a great communicator and an individual personally committed to advancing the university and further expanding our diverse and inclusive community and shared values,” she wrote. 

Nan Chen works on model for predicting Indian Monsoons


New research from an NYU/Abu Dhabi team has found that temperatures in the Atlantic are having a growing effect on the Indian monsoon, something that could prove crucial in predicting how severe rains are likely to be.

The study comes as climate change alters the patterns of monsoon rainfall in India, with likely far-reaching effects on agriculture, the economy and society.

In the latest study the team, which includes Nan Chen as well as 3 other NYU/Abu Dhabi researchers (Sabeerali CT, Ajayamohan RS, Bangalath HK) looked at the relationship between sea-surface temperature variability in the Atlantic and variability in the Indian summer monsoon.

Colder sea-surface temperatures in the eastern tropical Atlantic, linked to a weather system called the Atlantic Zonal Mode (AZM), tend to be associated with stronger monsoon rains.

The colder temperatures over the Atlantic strengthen the waves into the Indian Ocean, which increases the difference in upper atmospheric temperature between the Indian Ocean and the Indian continent. This causes more powerful moisture-laden winds to blow onto the land, leading to greater monsoon rains.

Link:  https://www.thenational.ae/uae/science/new-weather-model-to-spot-india-s-massive-monsoons-coming-1.862462

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