Monday, February 6 2023, 3:30pm 4th floor department lounge in Boyd building VISITS BY FORMER MEMBERS OF THE DEPARTMENT: Andrew Granville, University of Montreal, February 5-7. Carl Pomerance, Dartmouth, February 5-9. Monday February 6, at UGA, Boyd 328. Refreshments at 3:30 in the departmental lounge on the 4th floor. First talk at 4:00 by Andrew Granville (University of Montreal) What makes a proof acceptable? In the first year of university mathematics we are taught about the axiomatic structure of mathematics, how we build a solid structure of correct statements and their proofs, that can lead us to the stars (modulo Godel). We are taught that every correct statement can (and should) be justified back to the axioms. Working research mathematicians build their work on libraries of published material and hope that everything quoted is justifiable back to the axioms, so that their new contribution is also. This is also how new work is judged so if the system works perfectly then this satisfies the axiomatic dream, even though most researchers have little interest in going back to the axioms themselves, indeed much of the work that would be necessary to do so would be irrelevant. However we are all familiar with proofs that are a little shaky, perhaps missing a few details for us to be 100% sure, or even with a hole that "seems fillable". Professional mathematicians work with a notion of "robustness of proof", that even if a few details are awry one can be confident of the big structure. Thus even statements with a (formally) incorrect proof form part of the accepted literature, which seems like an odd way to proceed. How should the successes of proof verification software affect the community's view of what constitutes a correct proof? How will it? In this talk we bring together several threads to investigate these questions, and propose some objectives for the future. Second talk at 5:15 by Carl Pomerance (Dartmouth) Digits A low-brow area in number theory is to consider problems based on the digits of a number. However, there has been some highly nontrivial and interesting work involving digits. This talk will survey some of these problems and results. Ronald Burthe, UGA PhD 1995, NSA, February 5-6. Jon Grantham, UGA PhD 1997, IDA Center for Computing Sciences in Bowie, February 5-6. Alex Rice, UGA PhD 2012, Associate Professor, Millsaps College, February 5-6. Jim Stankewicz, UGA PhD 2012, IDA Center for Computing Sciences in Bowie, February 5-6. Sungkon Chang, UGA PhD 2005, Professor of Mathematics, Georgia Southern University, February 6. Kevin James, UGA PhD 1997, Director of the School of Math. and Statistical Sciences, Clemson Univ., February 6. Lee Troupe, UGA PhD 2016, Assistant Professor, Mercer University, February 6. Gerard Awanou, UGA PhD 2003, Professor of Mathematics, University of Illinois at Chicago, February 7. Victoria Baramidze, UGA PhD 2005, Professor of Mathematics and Chair, Western Illinois Univ., February 14. Daniel Mckenzie, UGA PhD 2019, Assistant Professor of Mathematics, Colorado School of Mines, February 21.
