AMSI supports eminent international researchers through the scientific program and its co-sponsorship of the Australian Mathematical Society’s biennial Mahler Lecturer program.

2019 Mahler Lecturer: Dr Holly Krieger

Mahler Lecturer

The Mahler lectures are a biennial activity organised by the Australian Mathematical Society, and supported by the Australian Mathematical Sciences Institute, in which a prominent mathematician tours Australian universities giving lectures at a variety of levels, including giving several public lectures.

In 2009 AMSI and AustMS partnered with the Clay Mathematical Institute, to combine the Mahler Lectures and the Clay Lectures into the Clay–Mahler Lecture Tour.

Biography

Dr Holly Krieger is currently the Corfield Lecturer at the University of Cambridge and a Fellow at Murray Edwards College.

Born and raised near Chicago, Dr Holly Krieger completed the undergraduate mathematics honors program at University of Illinois at Urbana-Champaign. She went on to a master’s degree and a Ph.D. from the University of Illinois at Chicago. Her initial research interests during graduate school were primarily in arithmetic and Diophantine geometry. Under the guidance of Laura DeMarco and Ramin Takloo-Bighash, her thesis work focused on the emerging field of arithmetic dynamics, which studies the relationship between dynamics of one complex variable and the arithmetic geometry of abelian varieties.

She followed her PhD work with an NSF postdoctoral fellowship at MIT under the supervision of Bjorn Poonen, during which time she became particularly interested in problems of unlikely intersections in complex dynamics. Since 2016, she has been the Corfield Lecturer at the University of Cambridge as well as a Fellow at Murray Edwards College.

https://www.dpmms.cam.ac.uk/~hk439/about.html

Tour Program
DATE TIME* TITLE VENUE STATE
22 November 3.00pm Mahler Lecture: Transcendence and dynamics UNSW, Sydney. Room RC-4082, School of Mathematics and Statistics NSW
25 November 4.00pm Mahler Lecture: Transcendence and dynamics University of Newcastle. Life Sciences Lecture Theatre NSW
26 November TBA Mahler Lecture: abc for the working mathematician University of Sydney. Room TBA NSW
27 November 2.00pm Seminar: Number theory (title TBA). University of New South Wales. Room TBA NSW
28 November 11.00am Seminar: Algebra and topology (Title TBA) Australian National University. Seminar Room 1.37, Hanna Neumann Building ACT
28 November 4.00pm Mahler Lecture: Elliptic curves and complex dynamics Australian National University. Seminar Room 1.33, Hanna Neumann Building ACT
29 November 4.00pm Mahler Lecture: Transcendence and dynamics UNSW Canberra. Room G23, Building 26 ACT
2 December 6.00pm Public Lecture: A tour of the Mandelbrot set The University of Melbourne. Room TBA VIC
3-6 December NA AustMS Plenary Lecture (Date TBA). (Title TBA) Monash University, Clayton campus VIC
9 December TBA Seminar: abc for the working mathematician The University of Queensland. Room TBA QLD
9 December TBA Public Lecture - The mathematics of life The University of Queensland. Room TBA QLD
13 December 11.10am Seminar: Differential geometry (Title TBA) The University of Adelaide. Room S12, Engineering North Building SA
13 December 2.10pm Mahler Lecture: A tour of the Mandelbrot set The University of Adelaide. Room LG28, Lower Napier Building SA
19 December 2.00pm Mahler Lecture: A tour of the Mandelbrot set University of Western Australia. Blakers Lecture Theatre WA

*(all times reflect host local time)

Please note: Mahler Lectures will involve some technical mathematics however are suitable for attendees with a broad science knowledge. All are welcome to attend

Talk abstracts

A tour of the Mandelbrot set

The beautiful and complicated Mandelbrot set has captivated mathematicians since the first computer images of the set were drawn in the 1970s and 1980s. In this talk we’ll take a walk around the infinite intricacies of the Mandelbrot set, exploring the spirals, finding Fibonacci, and answering the question every maths student wonders when they first meet the Mandelbrot set: why do we care about this pretty picture?

abc for the working mathematician

The abc conjecture, formulated in the 1980s by Masser and Oesterlé, is one of the most important conjectures in number theory, and most discussed conjectures in mathematics in the last decade. Often omitted from this discussion is the justification that the abc conjecture among one of the most interesting problems in mathematics. We will discuss some of the non-number-theoretic connections to and implications of the abc conjecture and related Diophantine questions, and explain why mathematicians in any field should care about this simple and deep number-theoretic assertion.

Transcendence and dynamics

Many interesting objects in the study of the dynamics of complex algebraic varieties are known or conjectured to be transcendental, such as the uniformizing map describing the (complement of a) Julia set, or the Feigenbaum constant. We will discuss various connections between transcendence theory and complex dynamics, focusing on recent developments using transcendence theory to describe the intersection of orbits in algebraic varieties, and the realization of transcendental numbers as measures of dynamical complexity for certain families of maps.

Elliptic curves and complex dynamics

In the last decade, an exciting program has emerged connecting the arithmetic of elliptic curves to classical questions in complex algebraic dynamics; that is, the study of iteration of maps on complex algebraic varieties. We will discuss this program and the fruit it has yielded, providing a new and surprising approach to fundamental questions about the interaction between geometry and arithmetic of elliptic curves.

The mathematics of life

Mathematicians and biologists are learning together how to describe and study the complexity of living things, revealing sometimes unexpected connections to fields of pure mathematics which include number theory and topology. We’ll discuss some of the most interesting such connections, and understand what mathematics has to say about the evolution and development of life in our world.