### Mahler lecture schedule

- Friday, 22 November: 15:00–16:00; University of NSW.

Public Lecture:*Transcendence and Dynamics*(more …) - Monday, 25 November: 16:00–17:00; University of Newcastle.

Public Lecture:*Transcendence and Dynamics*(more …) - Tuesday, 26 November: TBA; University of Sydney.

Public Lecture:*ABC for the Working Mathematician*(more …) - Wednesday, 27 November: 14:00–15:00; University of NSW.

Seminar: Number theory*TBA*(more …) - Thursday, 28 November: 11:00–12:00; Australian National University

Seminar: Algebra and topology*TBA*(more …) - Thursday, 28 November: 16:00–17:00; Australian National University.

Public Lecture:*Elliptic Curves and Complex Dynamics*(more …) - Friday, 29 November: 16:00–17:00; UNSW Canberra.

Public Lecture:*Transcendence and Dynamics*(more …) - Monday, 2 December: 18:00–19:00; University of Melbourne

Public Lecture:*A tour of the Mandelbrot set*(more …) - Tuesday, 3–6 December: TBA; Monash University.

AustMS Plenary Lecture:*TBA*(more …) - Monday, 9 December: TBA; The University of Queensland.

Seminar:*ABC for the Working Mathematician*(more …) - Monday, 9 December: 17:30–20:00; State Library of Queensland.

Public Lecture:*The Mathematics of Life*(more …) - Friday, 13 December: 11:10–12:00; The University of Adelaide.

Seminar: Differential geometry:*TBA*(more …) - Friday, 13 December: 14:10–15:00; The University of Adelaide.

Public Lecture:*A tour of the Mandelbrot set*(more …) - Thursday, 19 December: 14:00–15:00; University of Western Australia.

Public Lecture:*A tour of the Mandelbrot set*(more …)

### Biography

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.

### Talks & 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.

*Transcendance 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.