International Conference On Fractals And Related Areas 2026

About ICOFARA 2026

The International Conference on Fractal Geometry and Related Areas (ICOFARA 2026) is a global event to be held on May 1 - 2, dedicated to exploring the rich and evolving field of fractal geometry. The conference will be held in a hybrid format, combining both in-person and online participation to foster collaboration and accessibility across countries and time zones.

Participants and speakers are welcome to join virtually or at one of several in-person hubs (to be able to join a hub you need an invitation), where groups can gather to attend sessions together. In the hubs either speakers will present live (and stream the talk), and others talks will be projected if the speaker is not in that hub.

Confirmed in-person locations (hubs) include:

• The University of British Columbia (UBC) — ESB 4133 (PIMS library), bring your UBC card to have access (or send a message to us if you are locked outside), Vancouver, British Columbia, Canada.

The UBC hub, would like to thank PIMS for giving us the location and  funds to cover coffee breaks and meals. 

• The University of Rochester (UR) — Rochester, New York, United States

Organizers and Scientific Committee: Alexia Yavicoli, Alex Iosevich

Local organizers at the UBC hub: Ignacio Andres Rojas Aravena, Natalia Mora Cuellar, Hein Thant Aunt

Local organizers at the UR hub: 

Invited Speakers to the UBC hub:

• (UBC hub, confirmed) Ignacio Andres Rojas Aravena (UBC) i.andres@math.ubc.ca

• (UBC hub, confirmed) Hein Thant Aung (UBC) heinta@student.ubc.ca

• (UBC hub, confirmed) Huub de Jong (UBC) huub.dejong@math.ubc.ca

• (UBC hub, online, confirmed) Samantha Sandberg-Clark (Ohio State University) sandberg-clark.1@osu.edu

• (UBC hub, online, confirmed)  José Gaitan (Virginia Tech) jogaitan@vt.edu 

• (UBC hub, confirmed) Natalia Mora Cuellar (UBC) natalia.mora@math.ubc.ca 

• (UBC hub, confirmed) Chenjian Wang (UBC) chjwang@math.ubc.ca 

• (UBC hub, confirmed) William O’Regan (UBC) woregan@math.ubc.ca 

• (UBC hub, confirmed) Madeline Forbes (UBC) mforbes3@student.ubc.ca 

Schedule:

Start time: 9 am in Vancouver = noon in NY

First break: 10:45–11:15 am in Vancouver = 1:45–2:15 pm in NY 

Second break: 12:45–1:30 pm in Vancouver = 3:45–4:30 pm in NY 

End time: 3 pm in Vancouver= 6 pm in NY

MAY 1 (UBC hub):

🎤 Opening

• 9:00 – 9:15 → opening and hub connections

🔹 Block 1 (Vancouver: 9:15 – 10:45, New York: 12:15 – 1:45):

• 9:15 – 9:45 → William O’Regan (UBC)

• 9:45 – 10:15 → Huub de Jong (UBC)

• 10:15 – 10:45 → Hein Thant Aung (UBC)

☕ Break 1: 10:45 – 11:15 (Vancouver: 10:45 – 11:15, New York: 1:45 – 2:15)

🔹 Block 2 (Vancouver: 11:15 – 12:45, New York: 2:15 – 3:45):

• 11:15 – 11:45 → Samantha Sandberg-Clark (online, Ohio State University)

• 11:45 – 12:15 → José Gaitan (online, Virginia Tech)

• 12:15 – 12:45 → Ignacio Andres Rojas Aravena (UBC)

☕ Break 2: 12:45 – 1:30 (Vancouver: 12:45 – 1:30, New York: 3:45 – 4:30):

🔹 Block 3 (Vancouver: 1:30 – 3:00, New York: 4:30 – 6:00):

• 1:30 – 2:00 → Chenjian Wang (UBC)

• 2:00 – 2:30 → Natalia Mora Cuellar (UBC)

• 2:30 – 3:00 → Madeline Forbes (UBC)

MAY 2 (UR hub):

🎤 Opening

• 9:00 – 9:15 → opening and hub connections

🔹 Block 1 (Vancouver: 9:15 – 10:45, New York: 12:15 – 1:45):

• 9:15 – 9:45 → Shantanu Deodhar

• 9:45 – 10:15 → Zhihe Li  

• 10:15 – 10:45 → Akshay Sant  

☕ Break 1: 10:45 – 11:15 (Vancouver: 10:45 – 11:15, New York: 1:45 – 2:15)

🔹 Block 2 (Vancouver: 11:15 – 12:45, New York: 2:15 – 3:45):

• 11:15 – 11:45 → Ella Yu 

• 11:45 – 12:15 → Pablo Bhowmik  

• 12:15 – 12:45 → Quy Pham  

☕ Break 2: 12:45 – 1:30 (Vancouver: 12:45 – 1:30, New York: 3:45 – 4:30).

Attending in-person the UBC hub:

Ignacio Andres Rojas Aravena, Hein Thant Aung, Huub de Jong,  Natalia Mora Cuellar, Chenjian Wang, William O’Regan, Madeline Forbes, Yuveshen Mooroogen, Kaining Jia, Kin Ming, Petr Kosenko, Ethan Armitage, Alexia Yavicoli, Mathias Barreto, Brian Marcus, Chengyu Wu

Titles and abstracts day 1 (UBC):

William O'Reagan: 

Title: Bourgain's projection theorem over normed divisionalgebras.

Abstract: Bourgain's projection theorem of 2010 over the reals is one of the most influential expansion results in analysis. It has seen many direct and indirect applications, including to theresolution of the Furstenberg problem in the plane and the threedimensional Kakeya problem. In this talk, we give a 'new' proof of this result, which easily extends over normed division algebras; this includes the p-adics, and the complex numbers.

Huub de Jong:

Title: Smoothness of Markov Partitions for Expanding Toral Endomorphisms

Abstract: "Markov partitions are a tool that allow one to study dynamical 

systems via a cover by a shift space, where the covering map is one-to-one 

almost everywhere (consider, for example, binary expansion and the doubling 

map on the 1-torus). There are many types of systems that admit Markov 

partitions, the most classic example being hyperbolic toral automorphisms. 

A classic paper of Bowen shows that in dimension 3, no Markov partition can 

have piecewise smooth boundary. This result was later generalized by 

Cawley.

We have proven an analogous result for the related case of expanding toral 

endomorphisms in dimension 2, which yields qualitatively different results 

depending on the eigenvalues of the matrix inducing the endomorphism. These 

non-smoothness results highlight a connection between symbolic dynamics and 

fractal geometry, and some Markov partition constructions explicitly rely 

on fractal techniques. I will discuss this connection, and highlight some 

avenues for future work. This is joint work with Chayce Hughes. "

Natalia Mora:

Title: Multiplicative density is valuation space

Abstract: 

In this talk, I will present a framework to study multiplicative structures on the natural numbers by encoding integers through their prime exponents, allowing us to translate multiplicative problems into additive ones. This leads to a notion of multiplicative density that can be analyzed via an associated evaluation space, yielding analogues of classical density results, including a version of Szemeredi’s theorem.

I will also describe a connection with ergodic theory, where sets of exponents are modeled as symbolic dynamical systems and density corresponds to invariant measure. This provides an approach to studying multiplicative patterns using tools like multiple recurrence. This is ongoing work, with directions including random models and further exploration of the ergodic perspective. Joint work with I. Rojas Aravena and A. Yavicoli.

José Gaitan:

Title: On volumes of simplices in intermediate dimensions.

Abstract: A variant of the Falconer distance problem asks for fixed $k\geq 1$ and $d\geq k+1$, how large does the Hausdorff dimension of a Borel set $E\subset\mathbb{R}^d$ need to be to guarantee that the set of volumes of $k+1$ simplices formed by points belonging to $E$ has positive Lebesgue measure. Shmerkin and Yavicoli established a stronger pinned result, namely that there exist $x_0,\ldots,x_{k}\in E$ such that $\Vol_{k+1}^{(x_0,\ldots,x_{k})}(E) = \lbrace \Vol_{k+1}(x_0,\ldots,x_{k},x_{k+1}) : x_{k+1}\in E \rbrace$ has positive Lebesgue measure with sharp dimensional threshold $\hdim E>k$ in the case when $d=k+1$. 

In this talk, we present recent work where we extend their result to $k+1 \leq d \leq 2k$ and obtain a non-trivial dimensional threshold $d-k$ when $d>2k$. The result is motivated by ideas from Shmerkin and Yavicoli. A crucial part of the argument is an application of work by Bright, Ortiz and Zakharov on A Continuum Beck-type Theorem for Hyperplanes as well as the classic results of Marstrand's on Projections and Slicing Theorems. 

Ignacio Rojas:

Title of the talk:"A non-linear generalization of the Kakutani Equidistribution problem".

Abstract: Take the unit interval [0,1] and a number a between 0 and 1. At each step, split every interval of maximal length into two pieces in proportion b : (1-b). This recursive scheme is known as the Kakutani splitting procedure and in 1976 it was proved that the sequence of partitions becomes equidistributed. In this talk we will explore a nonlinear generalization of this problem and sketch how the proof works.

Madeline Forbes

Title: Kakeya-like sets in finite fields

Abstract: Given a set that is "large" in the sense that it contains many copies of a geometric pattern, it is natural to ask if there is a quantitative sense in which the set must be large. For example, the well-known Kakeya problem studies sets in Euclidean space containing a unit line segment in every direction, and seeks a lower bound on their Hausdorff dimension. In this talk, we consider problems of this type in the less classical setting of finite fields. In particular, we will discuss previous results of this flavour and provide an overview of the polynomial method which has produced many of these results. We extend a result of Trainor, which provides a lower bound on a class of sets containing a one-parameter family of codimension one algebraic varieties, by providing the same lower bound on an analogous class of sets containing a k-dimensional family of codimension k algebraic varieties.

Chenjian Wang:

Title: Weighted estimates for circular averages

Abstract: We prove mixed-norm estimates for circular averages with respect to $\alpha$-dimensional fractal measures on $\mathbb R^2$, using circle tangency bounds when  $\alpha in (0,1]$, and a $\delta$-discretized slicing lemma for fractals when $\alpha in (1,2]$. As applications, we obtain new exceptional set estimates for the radial integrability of functions in Lebesgue spaces, as well as for the H\"older regularity in time of solutions to the linear wave equation on $\mathbb R^2$.

Samantha Sandberg Clark:

Title: Introduction to Thickness and Finite Point Configurations

Abstract: In this talk, we introduce Newhouse thickness as well as tools and techniques—such as the Gap Lemma—used to determine finite point configurations in sets of sufficiently thick compact sets of R and R^d.

Hein Thant Aung : 

Title: Simultaneous Avoidance and Inclusion of Patterns in Fractal Sets

Abstract: In this talk, we will talk about pattern inclusion and avoidance problems in fractal setting. Some recent works of Fox, Pohoata and Roche-Newton constructed subsets of the integers that avoid 4-term arithmetic progressions, but contain many 3-term arithmetic progressions simultaneously. We will discuss how these constructions can be generalized and how they can be lifted to the continuum. More precisely, given finite subsets $P$ and $Q$ of the integers, we will discuss the problem of finding a full-dimensional subset $E$ of $[0, 1]$ that avoid affine copies $P$ but include full-dimensionally-many affine copies of $Q$.

Joint work with M. Pramanik and A. Yavicoli.

Titles and abstracts day 2 (UR):

Shantanu Deodhar, University of Rochester. Title: Spectral synthesis with the complexity parameter. Abstract: Agranovsky and Narayanan proved that if a function $f \in L^p(\mathbb{R}^n)$ for $p \leq \frac{2n}{d}$ and its Fourier transform is supported on a $d$-dimensional sub-manifold, then $f \equiv 0$. We show that the exponent $p$ is governed by a quantitative spectral complexity parameter, the Fourier Ratio, in addition to the geometric size of the Fourier support. In the Euclidean setting, with additional information about Fourier ratio decay $\kappa$, the classical synthesis threshold improves from $\frac{2n}{d}$ to $\frac{2(n-2\kappa)}{d-2\kappa}.$ In particular, we show how the Fourier ratio naturally captures the curvature of the manifold, leading to a sharper integrability threshold. As an application, we compute $\kappa$ for a class of co‑dimension 2 manifolds in terms of their curvature, yielding an explicit improved bound. This demonstrates that the Fourier ratio captures curvature information and sharpens the synthesis exponent. 

Zhihe Li, University of Rochester. Title: Fourier Ratio in the Euclidean setting. Abstract:  In this talk, I will introduce a continuous analogue of the Fourier ratio for compactly supported Borel measures, defined as the ratio of the $L^1$ and $L^2$ norms of a regularized Fourier transform at scale $R$. This quantity interpolates between $L^1$ and $L^2$ Fourier information and connects uncertainty principles, Fourier restriction, and approximation by trigonometric polynomials. I will present sharp bounds in terms of geometric properties of supports, discuss several interesting examples, and derive a fractal uncertainty principle. 

Akshay Sant, University of Rochester. Title: The Mobius function and learning theory. Abstract: We are going to discuss some connections between the Mobius function and learning theory. In particular, we are going to show using the Fourier ratio, some recent exponential sums estimates, and Vapnik Chervonenkis theory that a natural class of functions that includes the Mobius function restricted to [1,N] cannot be learned in fewer than CN steps. 

Ella Yu, University of Rochester. Title: Generalized Salem sets and Bourgain's inequality. Abstract: In classical Fourier analysis, Salem sets are characterized by uniform bounds on the Fourier transform. In recent work, Jonathan Fraser introduced a framework that replaces such $L^\infty$ bounds with $L^p$ average estimates of the Fourier transform, leading to a natural generalization of Salem sets in the finite field setting. In this talk, I will present this perspective, discuss several examples, and explain its connections to sumset problems and Fourier restriction theory. I will also highlight how this framework is related to Jean Bourgain’s $\Lambda(p)$ inequality. 

Pablo Bhowmik, University of Rochester. Title: TBA

Quy Pham, University of Rochester. Title: Fourier Integral Operators, Point Configurations, and Elekes-Ronyai Type Problems. Abstract: In this talk, I will discuss results showing that various $k$-point configuration sets of thin sets have positive Lebesgue measure, obtained by exploiting optimal $L^2$-based Sobolev estimates for the associated family of Fourier integral operators. Extending the framework developed by Greenleaf, Iosevich, and Taylor, we obtain Falconer-type results for many configuration sets for which the method would be vacuous if one were to demand nonempty interior.